Archives for October 2012
Calculus Cheat Sheet: EveryStepCalculus.com
Use the TI-89 as the Ultimate Cheat Sheet
..
My name is Tom and I program TI-89 calculators to be the Ultimate step by step Calculus Cheat Sheet. The app show all work right on the calculator screen.
The programs are a Compilation of Midterms, Final Exams and homework from college calculus classes 1,2 and 3 all over the United States. The app shows work for calculus solutions line by line at your own pace so you can write it down on tests, homework, whatever.
You get all the calculus 1,2 & 3 programs below for the price of a serious happy hour. That all four years of calculus, updates forever included.
100% Guaranteed or your money back
LEGENDARY SUPPORT:
Phone Support (my favorite) | Email Support | Facebook Support | Twitter Support
I do it ALL and it is IMMEDIATE!
CALCULUS 1 PROGRAMS (Scroll down for 2 & 3)
Chain Rule | dy/dx = f’[g(x)] * g’(x) | dy/dx = f’(u) * u’ | (5x²+7)^5 | sin(ax) | 7*cos(5*x^2) | (tan (5x))^5 Video Example
Concavity
cos(a * x) derivative
cos(a * x) integrate
Critical Points Video Example
Definite Integral | = ∫ [ f (x) ] dx Video Example
Definition of a Derivative
Derivatives/Algebra (step by step) | √(x) | 3√(x) | 5/√(x) | 5/x | 5/8x | 5/x² | (5x)² | 5x²/8 | x(x+5) | x^½ | x^(-½) | (x²-4)/(x+2) | (x²-4)/(x-2) | (5x²+7)^5 | √(5x²+7) | (5x²+7)½ | ³√ (5x²+7) | (5x²+7)¹/³ | sin | cos | tan
Difference Quotient Video Example
ê(x) Derivatives
ê(x) Integrals
Equation of a Tangent Line (y=mx+b) Video Example
Equation of a tangent line at a pt | (y = mx + b) Video Example
Graphing by Hand | Concavity | Critical Points | Crosses x axis | Inflection Point | Intervals of Increase | Intervals of Decrease | Local Max & Min
Local Max and Min Video Example
Implicit differentiation | y³+y²-5y-x² = -4 Video Example
Integrals/ Algebra (Rewrite selected & Integrate) | n / √(x) | (x² + n)² | (x³ + n)/x² | ³√(x) | n / x² | n / ³√(x) | n / x√(x) | 1/x³
Integration by Parts | ln(x) Video Example | n*e^x Video Example | sin(x) Video Example | cos(x)
Intervals of Increase or Decrease
Limits Video Example
In(x) Natural Log
log(x) Log to Other Base | Evaluate | Solve for x | Exponential Form | Logarithmic Equation | Differentiate
Product Rule | ( f (x) )( g (x) ) Video Example
Quadratic Formula
Quotient Rule | ( f (x ) ) / ( g (x) ) Video Example
Relative Extrema
sin(a*x) Derivative
sin(a*x) Integral
Trig & Half Angle Formulas & Identities | cos(2x)2 | 1-cos(2x) / 1+cos(2x) | sin²(x) + cos²(x) = 1 | tan(x) | tan²(x) | Trig d/dx cos(2x)/2 | cos(2x) | cos(x) | cos²(x) | cot(x) | csc(x) | csc²(x) | sec(x) | sec²(x) | sin(2x) | sin(x) | sin²(x)
Trig d/dx Identities
U – Substitution
Recent Testimonials Summer 2013:
Tom- I showed my ex, who is a calculus professor, and he was waaaaaaay impressed. And he is an arrogant ass, who never helped me ever…I could tell he wanted to hate on it, but he couldnt.
Kristin P
Tom…I think that I’m finally done with Calculus II. In the prior test I got 78 and yesterday I finished all the problem on the test. I think I should be able to remain around the same grade. Thank you so much for your help; your programs really made the difference. They didn’t just solve the problems for you, in my case, they gave me the confidence and security I had lost with those stupid professors and the way they teach. To be honest, studying the programs on my calculator taught me how to solve problems that I couldn’t do before due to the way they were presented. I felt confident and secure yesterday, and it only possible because either I remember how to do the problems or the calculator would. Thanks one more time for time, dedication and quick responses. There is no other person in the whole world that would do what you do for us , college students being killed with freaking calculus classes. John
Tom- Got it to work with that link you sent me! Just wanted to say thanks for all the great work you do, and for helping me pass this calculus class. I’m going to tell everyone about this and make them pay the $30 dollars because you have done a splendid job programming my friend. Let me know if you have any new programs for derivatives or integrals and Ill let you know if I need any more help! Much thanks, –Eric
I basically just needed to say that you’re an amazing man. Basically saved my life during my emag theory course
-DoubtingThomas (Youtube vectors review here)
oh my god I figured it out. You’re the freaking best! -Sarah
Thanks Tom. I appreciate you taking the time to break down and explain these to me. :0) –Nelson
Tommy, Great talking with you last night. I already liked you for developing this “most excellent program” but after our conversation I concluded you to be a great guy. I’ve been playing with this program most of the night, took in a few “z’s” and am back for more. This program really is superb. I did, however, notice that for some unknown reason when I attempt to do Relative Extrema’s and Trajectories that both programs came up as “Program not Found”. I’m not sure if I will be encountering the Trajectory stuff in this semester of Calculus but I do have a test this Thursday that includes Relative Extrema. Any suggestion, oh Master of this great creation?! I’m going to be gone most the day but should be home late afternoon if you got time to call. Same number (843-xxx-xxxx). That’s Myrtle Beach, 3 hours ahead of you and more golf courses than you can shake a stick at. Thanks -Joe
Wow! Awesome! These are great, so great, thank you! -Kristen
Tom is the man! His program is helping me pass my calculus class. He was willing to help me immediately when I couldn’t get one of the programs working! This application is in my opinion a STEAL! I’ve never met Tom in person but I’ll owe passing this class to every step calculus.
-YouTube product rule video comment
CALCULUS 2 & 3 PROGRAMS
A & B Vectors A(x,y,z) B(x,y,z) ||A|| Magnitude ||B|| Magnitude | A – B | A – B Magnitude | A + B | A + B Magnitude | A + B + C | Find Resultant | Find Components | A * B Dot Product | | A x B Cross Prod | B – A | n * A | (n * A) + (n * B) | Area of a parallelogram | Component A direct B | cosine(AB) | Equation of a Plane | ax+by+cz+d=0 | P&Q Points | Projection of A on B | Projection of B on A | Unit vector A | Unit vector B Video Example
Acceleration | r(t) function
Angle of a Vector | r(t) function
Arc Length | f(x) system | r(t) system | y system
Average Rate of Change
Component of A Direction of B
Conservative Curl
Compute Curl at a Point
Compute Divergence at a Point
Cosine(∅) of A & B
Curl | Definition | PQR notation | Conservative | Divergence | Curl Problem | Compute Curl at Point | Compute Divergence at Point | MNP notation | Conservative | Divergence | Curl Problem | Compute Curl at Point | Compute Divergence at Point Video Example
Cross Product Video Example
Definite Integral Video Example
Divergence of Curl
Divergence of Vector Field
Dot Product Video Example
Eliminate the Parameter (t)
Gradient | Definition | 2 Variables | 3 Variables
Implicit Differentiation Video Example
Trig & Half Angle Formulas | 1 + cos(2x)2 | 1 – cos(2x)/1 + cos(2x) | 1 – cos(2x)/2 | cos(2x) | cos(x) | cos²(x) | cot(x) | csc(x) | csc²(x) | sec(x) | sec²(x) | sin(2x) | sin(x) | sin²(x) | sin²(x) + cos²(x) = 1 | tan(x) | tan²(x)
Linear Equations (3 variable) | ax+by+cz+d=0
Line Integral Over Range | = ∫ ( f [(x(t),y(t),z(t)] * √ [ x'(t)² + y'(t)² + z'(t)² ] ) dt
Mass of Spring or Wire
Magnitude of a Vector | r(t) function
Parametric Equation | r(t) function
Partial Fractions Integration
Polar to Rectangular Conversions
Projection of Vector A on Vector B
P & Q Vector Points | Position Vectors | Projection of a on b, b on a | Speed
Quadratic Formula
Sketch a Graph | r(t) function | Make a Table of Points
Surface Integral | x,y | x,z | y,z
Position Vectors | Velocity | Acceleration | Speed | Unit Tangent Vector | Parametric Equation | Standard (Linear) Equation
Speed | r(t) function
Sphere | Center Point | Mid Point | Equation | Radius
Surface Area Revolving
Surface Integral | x,y | x,z | y,z
Tangent Plane to a Surface
Trig d/dx – Identities and Functions | Half Angle Formulas | Reciprocals | Integration | Derivatives | 1+cos(2x)2 | 1-cos(2x) / 1+cos(2x) | 1-cos(2x)/2 | cos(2x) | cos(x) | cos²(x) | cot(x) | csc(x) | csc²(x) | sec(x) | sec²(x) | sin(2x) | sin(x) | sin²(x) | sin²(x) + cos²(x) = 1 | tan(x) | tan²(x) Video Example
U Substitution
Vectors | Unit Tangent Vector | Unit Vector PQ/||PQ|| | Vector Between P & Q
Velocity
Volume of a Parallelepiped
Work | Force Field | Lifting Object | Spring | Pumping Oil
Don’t forget the programs come with my
LEGENDARY SUPPORT:
Phone Support (my favorite) | Email Support | Facebook Support | Twitter Support
I do it all and it is immediate.
………..[ahm-pricing-table id=1330 template=gray]
Calculus Cheat Sheet Video Transcript
Chain Rule Calculus | Video | EveryStepCalculus
Raw Transcript
Chain Rule, If you see in a given problem, a function with a square root sign, or a function enclosed in parenthesis where that function is taken to a higher power in other words has an exponent, or a trig function such as sin, cosine, or tangent where there is something more than an x in the parenthesis of that trig function, you are using the chain rule. To get to my menu, you have to press second alpha on the Titanium to enter letters in the home screen, and then you enter the letters
ex press alpha again and enter the eight and the closed parenthesis. Press ENTER and you’re into my menu. You choose “chain rule” by scrolling down to it, or pressing the number before it, in this case the number six. Then press ENTER. You are given three things to choose from here. One, Anything enclosed in parenthesis to a power Two, If you are already given u and f of x And Three, the trig functions with something more than an x involved. I’m demonstrating the third option in this video, the trig function. Enter your trig function. Press alpha first, then the second button, I’m going to do tangent. Three times x squared. I show you what you’ve entered You can change it if you want I say it’s ok You write all of this down on your paper or homework Here’s the formula Here’st he choice for u Here’s what f of u And you’ll notice one over cosine u squared This is an identity for secant squared, the derivative of tan of u Identities, derivatives and integrals of trig functions can all be obtained by going to trig d d x in my main menu And the next screen is the step by step answer Pretty neat huh? Everystepcalculus.com. Enjoy my programs and pass calculus.
Calculus Help Video
Calculus Help using ti-89 video transcript
Calculus Help
7/sqrt(t) |
State the domain of the function. (Enter your answer using interval notation.)
State the domain of its derivative. (Enter your answer using interval notation.)
Hello Brandon, any time you see a division sign or times sign when thinking of differentiation, first you think of converting somehow to get rid of the division or times sign. In this case the definition of derivative formula is always in x so you need to think maybe of changing the variables. t to x’s so: f(x) = 7/√(x), next since the numerator is only a constant this is not a quotient rule problem, however I realize that you are told to use the definition of derivative to get the answer. You still need to convert before you try that, so: f(x) = 7*x^(-1/2). To find the derivative you’d take the exponent (-1/2) and multiply it times what ever’s in front of the x in this case 7 to get -7/2, then take 1 away from the exponent -1/2 or: -1/2 – 2/2 = -3/2 this will give you -7/2*x^(-3/2), then convert to -7/2/x^(3/2). Now as far as my programs go I haven’t programmed that because I don’t think it would appear on any test. If it did everyone would flunk it probably. Let me know what you think, Tom
Calculus Help: ln(x) differentiating program
Calculus Help: ln(x) differentiating program
Hi Tom,
- If , find
3. If , find
What Professors don't tell you about ln(x)
Any problem with ln(x) in it you’d choose ln(x) in my program menu
When differentiating ln(x) and when using the product rule which is necessary, where the function might be something like 5*ln(6x). You have two functions –—— 5 and ln(6*x). Two functions mean f(x) and g(x).
In my programs I used in this case 5 for f(x) and ln(6*x) for g(x)
And you have the formula for product rule, h ‘ (x) = f ‘(x) * g(x) + f(x) * g ‘ (x)
Don’t worry – I do all of this for you – step by step – in my programs, however I want to mention here of again what professors don’t tell you or make you aware of, and that is
If ln(x) has a + sign or – sign in it, it makes a difference which one you use for f(x) or g(x) so for instance in a function like 5*ln(6x+1), you have to use instead of 5 for f(x) (like above) — ln(6x+1) for f(x)
Now who told you or me about that little detail in our calculus life?
Incidentally any derivative for ln(x) has a special formula which is:
u ‘ / u
u is what’s inside of the parenthesis.
Have fun with my programs and pass calculus, never to use it again !!!
Tom
U Substitution Practice | TI 89 App | Every Step Calculus Video
Raw Transcript
This is a video solving a u substitution problem step by step and also demonstrating how my downloadable programs work in your TI 89 Titanium calculator and other TI calculators for calculus and physics problems and let’s get started here to access my programs you have to press second alpha and put the i n d e x letters in here and then press alpha again to put the eight and the open and closed parenthesis press enter you’re into my menu, many things to choose from here as you can see definite integral critical points graphing by hand chain rule we’re going to go up here with the curser to get down to the bottom of the menu which is u substitution and we’re going to put in our function you have to press alpha again to put anything in these entry lines remember to do that alpha let’s go five times x times sign of three times x squared. I always show you what you’ve entered you can change it if you want. I say it’s ok and we’re going to evaluate this of course you have to bring the constants outside the integral which I do for you any time there’s that plus we want to bring this x now over by the x dx to make sure it’s a u substitution problem somehow this inside of this parenthesis has to be made to match this I choose that for you here’s the du you always take a constant out of here and du divided by six and then isolate the x dx which you can see is the same so this is a valid u substitution if it wasn’t it’d be an integration by parts problem. I make sure you know that so I have to ask you this does x equal x it checks whether that is a u substitution problem and here’s your answer you write all of this down on your paper exactly like I’ve got it here you’re bringing constants outside the integral you’re multiplying times what you’ve put outside the integral before, and here’s the answer right here minus five sixths times cosign of three x squared plus c. Pretty neat, huh? everystepcalculus.com. Go to my site buy my programs and pass calculus.
Calculus Solver Software | Solve Calculus Problems | App
Raw Transcript
Ok this is a video on a calculus solver for calculus problems, my programs are
perfect for solving all kinds of solving calculus questions and problems. The are
designed for tests really, I’m not interested that you learn it or that you memorize
it, I am interested that you learn enough to pass tests and get out of calculus
somehow. That’s what my programs were designed for me to do, and hopefully
for you if you purchase them. Anyways let’s get started – you press second
alpha to put the I n d e x in the calculator, then you push alpha eight and closed
parenthesis to get to my menu, then you press enter and up comes my menu.
You can scroll down for many, many different things. I have graphing by hand, ya
know, concavity and vectors where you can put in a and b vectors. Here’s cos of
a and b which is two vectors, and you find the angle of it. Definite integral,
Definition of derivative, which is pretty interesting. Equations of lines, integrate,
gradient, graphing by hand, implicit differentiation, Inflection point, graphing by
hand, limits, line integral, log – p and q points – P and Q points is interesting
because that’s in calculus three really, because they give you the end points and
these vectors show direction, where the other vectors show just, they are really
called scalars, but this is actually a directional vector, when you get p and q
points, x y and z variables. Well let’s do p and q points here to see what
happens. Wait for it to load here, and you’re going to put the – you’ll notice your
going to have to put the x value in, you’re going to have to press alpha and put
eight, that’s what they’ll give you in test, and then you are doing the y value, and
so your going to put alpha minus nine, and then alpha, I don’t know maybe put
four in here. An then we’re going to do the q point of the vector, again alpha,
let’s go minus five, alpha minus eight, and alpha ten. I show you the points, what
you’ve entered, see if you want them right, you look at your test to see if you’ve
entered them correct, and then if they’re correct, we press ok, and we can do all
kinds of these different things, sphere equation, we can do sphere radius, we
can scroll down to sphere radius – sphere remember is calculus three because
we’re into spheres, which are three dimensional things. Here we have the mid
point, we can go mid point here. Center of a sphere is a mid point and it’s given
by pq, I give you the formulas, and here we have four minus eighteen over two,
and then calculates to that vector. Standard equation, press five, these are all
standard equations – center point, press two, center of a sphere is the midpoint
and is given by pq, there’s the center again, we already did that. Radius, there’s
radius, it’s a square root and then squares within the square root, approximately
seven point eighteen units. So make sure that when you look for a calculus
solver, that you are looking at my programs, because on the Titanium there is no
better solver for calculus than what my programs do, people have said that over
and over again. Every step calculus dot com, check it out.
What Calculus Professors don’t tell you about e^(x)
One of the toughest things to do in calculus is to recognize or recall what to do with a given problem in order to solve it. Professors tell you about the problem their trying to teach but they don’t tell you about the subtle differences, what to do if this happens or is changed.I was programming – integrating e^(x) problems on the Titanium or TI-92+, or Voyage 200, for you folks using integration by parts and was really proud of myself – the step by step answers for most problems were coming up using the formula u*v – ∫(v*du) — all of sudden there were wrong answers compared with what the calculator was coming up with using its integral program or system. Why?? So here’s what I find, and have written another program to handle it. Remember I don’t program to learn or teach calculus – I program to pass the pathetic tests, to pass the class, and get hell out of there, never to touch the subject again. So:Anything with e^(x) or e^(ax) (“a” being some arbitrary number) even when connected to sin(x) or tan(x) or ln(x) etc is an integration by parts problem.
However:
Integrating anything with e^(x^2), e^(3x^2), e^(3x-1), e^(5x+6) is U- substitution.
To make it clear — if there is an exponent within the exponent of e, or if there is a minus sign or plus sign within the exponent of e you are using U- substitution.
Now isn’t that fun!! What professor told you about that in class. When I program this stuff – I (and the program) have to know those differences, the program has to work line by line, step by step with the best system possible to solve the problem logically and correctly. Enjoy my programs!
Arc Length Tutorial on the TI-89
RawTranscript
This is a program on arc length, and let’s get started. To get my code in here to get my menu to come up, you have to put the letters i n d e x, which you do by pressing 2nd alpha, on the Titanium first for the letters and then alpha and you can enter the eight and closed parenthesis on there, press the enter button and you are into my menu. Here’s all the choices goes way down here, you can find all kinds of things on here which will help you out in your test, your homework, or just leaning about it, because its so perfect step by step, and it’s all what we wished we could have when we were looking on how to do a problem. That’s why I did it for myself first and now am offering it to you. Let’s do arc length, were going to press the number four here and get into the parametric form which is the r t form with time and radius, and three variables x y and z in this one. And this one is the Cartesian system which is equal to y = f of x, either one will give you the function there. And so we’re going to press two and enter a function. Press alpha and let’s put the function in here, we’re going to go, x cubed divided by six plus one divided by parenthesis two times x, closed parenthesis and over the range of – we have to add alpha again to get the range in here – we’re going to do it, one half to the upper range of two. It shows you what you’ve added here so you can correct it if it’s wrong or check it out here. I say it’s ok so we’re going to press one – derivative of the function here, with respect to x is x squared over two, minus one over two x squared. Here’s the formula for the arc length, the integral over the range of a and b, the square root of one plus dy dx squared, and with the respect of x. Here we have the function into the formula here, this is the part that was squared, here’s what we did the dy dx part, which we found before, mark all of this on your paper of course. Here we’ve taken the square of that, still have the square root to do, one plus, but we’re going to take the square first, like you would in normally doing a problem, here we added the one to it, here we’re going to do the square root of it, which is this. Working the formula through, here’s the, as we integrate it, here’s what the integration is over the range of two and minus one half. We put the two in the problem, two to the four minus three over six times two, which I show you here, equals thirteen twelve’s and we put the one half in here, we subtract the lower from the upper, and we added the half into the formula, here’s minus forty-seven forty-eight. And we can see that we had a minus forty seven, this will trip you up a lot of times, where there’s a minus to a minus, I do it to make sure it doesn’t happen to me, when I’m doing the problem. Thirteen twelve’s plus forty seven forty eight, the answer is thirteen sixteenths, approximately two point zero six two five, rounded to the fifth place. So pretty neat huh, everystepcalculus dot com, check out my other fabulous programs, you’ll love them, worth every penny that you buy it for, so cheap compared to the thousands of hours I’ve spent on this stuff studying it for you, to make sure they are correct and everything, and remember it encompasses calculus two and three and one, so you are buying all three semesters of your calculus in one purchase, ahh have a good one.
Calculus Video – Inflection Point – Graphing on the TI89 Titanium app
Raw Transcript
Ok, this graph is on inflection points, or inflection point of a graph, and let’s get started – you put index8 in here, ya know, second alpha for the letters and then Alpha eight, closed parenthesis, and that’s the code for my menu to come up, and here’s the menu, of all different things that I’ve programmed so far, so we want inflection point – so we’re going to scroll down here, there all in alphabetical order, so were going to scroll down to inflection point there – press enter – and you can see that this is graphing by hand, you have concavity, critical points, crosses the x and y axis, inflection point, intervals of increase and decrease, and local maximum and mins. All these come up in my graphing by hand program that I have designed. And so, I tell you to, ya know, mark of course on your graph paper or test this, ya know graphing, ah axis, and then we’re going to enter the function, so – you have to press alpha first – let’s enter minus x cubed plus three times x squared minus two, press enter twice, it shows you what you’ve entered – you can go back and change it if you want, I say it’s ok and I’m going to press number one, and you can get all these from that function, you can get all of these uhm different answers, so we want inflection point number six, I’m going to press number six and uhm, notice the way you do the inflection point, you take the first derivative and then you take the second derivative, here’s the six times x times x squared the first derivative and then the second is six minus six times x, and then we’re going to factor it, factor the second derivative and you get minus six times x minus one equals zero, so x equals one – x component of inflection point – and you plug that into the original function – I show you how to do that here – here’s y – the original function – and we’re going to put one in for x – here’s x cubed plus and plus one into three x squared, and when you compute that out it comes to zero – so the inflection point is really one and zero – x equals one and y equals zero – mark this on your pencil graph and label it, ya know, pretty neat huh, check my web site out – everystepcalculus.com.
Concavity Graphing on the Calculus App TI-89 Titanium Video Example
Raw Transcript
Calculus -Vectors – Program App – TI-89 Titanium Calculator
Raw Transcript
This is a video on vectors, and let’s get started here. You have to press second alpha to get to the letters of my menu code, i n d e x and then press alpha again and put in the eight and the closed parenthesis, and press enter and you are into my program, you’ll notice you can scroll down to get to the a b c’s of the beginning of it a and b vectors but you know that’s also goes to vectors but we can go, scroll down in case you want to call it just plain vectors, and we’re going to press enter and get into the vectors program. Press alpha before you put anything in here, were going to press alpha eight, alpha minus twelve, alpha nine, for vector b, the x y z coordinates, we’re going to put in alpha seven, alpha minus thirteen, and alpha minus fifteen, I tell you what you’ve entered so you can change it if you want, I say it’s ok, I’m going to press number one and we’re into all the different functions, if you want to find the magnitude of vector B, press three, and do the calculations, shows you what your doing here and you get absolutely do all the calculations, square root et cetera. We can go a plus b, number 6, a plus b, eight twelve, et cetera, come up with the a plus b answer. We can have a plus b plus c it’ll, three vectors find their resultant and components. We have to enter the vector c, alpha eight, alpha six, alpha minus two and again check whether we’re doing it, vectors a b and c , resultant, b minus a et cetera, let’s do the cosine, cosine between a and b, that’s the formula there, you write all this stuff on your paper of course, and we’re doing the dot product of it and then we’re doing the rest of the calculations, does all of the calculations for you, and gives you in radians or degrees. Pretty neat huh? Everystepcalculus dot com. Check out my site and purchase the programs if you want, and enjoy my programs.
Parametric Equations, Calculus Program, App, TI 89 Titanium
Raw Transcript
This video is on parametric equations. A parametric equation is, you’re adding a
parameter of t time to every x y and z function, and that’s where we add the
parameter and that’s the reason we call them parametric equations. And let’s do
it. Turn the calculator on here. We’re going to get back to the home screen here.
Clear the calculator we can go F1 eight and it clears that screen here. You press
second alpha and put in the letters i n d e x, and then you push alpha and get
into the number 8 and closed parenthesis to add this and get my formula for my
menu. Press enter and we’re into my menu. And you can see all the things
available in my menu for you to pass calculus and do your homework. Position
vectors, product rule, projection of a and b, all those kinds of things you will be
involved with in calculus one two or three. We’re going to do parametric
equations now. That’s concerned with position vectors. If z is not given you
enter zero in for z, then you can do the other two, x and y. So there’s the vector
r t is generally an r t, is equal to this vector here, x t, y t and z t. So you have to
press alpha to enter the functions in the entry lines here, so let’s do it, three
times t let’s say plus four for x t, here’s y t, let’s enter have to push alpha, five
times t and let’s do the z one, or let’s put alpha just for to make it simple and put
z you can see that the z one is zero. Gives you a chance to change it if you’ve
made a mistake, and we have all these things that we can do with this formula
now with these functions in there. We can eliminate the parameter. Which
eliminates the t and changes it back to an x function. Let’s do that quick, I’ll go
through these quick so you can see. You solve for t, here’s the solution for t, and
then you substitute t into every other x y and z, but ah here’s one point six seven
times x minus three point nine and that eliminated the t parameter. Let’s go
length of arc, you want to do that, fine, let’s go press four, notice it’s an integral
over a and b, with the derivative of the r t formula. And rt we’re going to put in
what we entered, I’ll go through it quick, put this all on your paper, write it down
exactly as you see it, and we’re doing the square of each one, over the time of
let’s say, you have to push alpha, let’s say from two to alpha six, shows you from
two to six, here we’re doing this, write this on your paper and each individual one
is gone, there it is, and here we substitute etcetera in there, and here we have
approximately twenty three point four units. We can do speed, do you wanna do
speed, let’s push number seven here and do speed, unit vectors or speed is the
square root of these squared. Square root of nine, twenty five zero. 5.8 meters
per second. Ah pretty neat huh? Everystepcalculus dot com, check it out. Go to
my site and you’ll love these programs.