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Hello, Tom from everystepcalculus.com,and everystepphysics.com. A problem in calculus dealing with critical numbers in critical points of a function. Let’s do it. Index 8 to get to my menu. Then your going to scroll down to critical point or numbers.I always have you start a graph on your paper. When you enter the function you have to press Alpha before you enter anything into these entry lines. Your going to press Alpha X cubed minus 3 times X. I always show you what you’ve entered. You can change it if you want. I say it’s okay. And we’re gonna choose number five, critical points.

Dear Tom,

I would like to know if your program also solves integrals consisting only of symbols like x, a or b in both definite and indefinite matters?

Example:

 or

Would solving does definite integrals be possible using your programs showing the solution process step by step?

Kind regards,

Ben

Answer 

The first integral, sounds like your professor didn’t teach you, so you will want my programs to teach you or me to teach you. A common endeavor in my experience. When you see the da that’s “with respect to” in other words, you are integrating that integral with respect to “a”.  In my programs you’d change all the “a’s” to x”s.

Now could you solve the integral if it looked like:       

  x                  x

∫ (1/x)dx   or ∫ (   1/[(c+b)-(k+x)]  ) dx

o                   o

Now these would never appear on a test unless your professor demonstrated them on the black board, so they are either homework or experimenting off the internet. Both integrals are definite integrals because they show a range to integrate over. When you solve the integrals you have the area under that functions curve. That’s all integrals do is solve area under curves. You can graph 1/x on your calculator and you can see what the first integrals function looks like. Now, anytime you see a function without an exponent in the denominator, it is a natural log answer. The reason is is that you can’t integrate term with a division sign.  

In this case the x has an exponent of 1 (  x^1), you always have to move the denominator to the numerator to eliminate the division sign before you can integrate. If you move the x^1 to the numerator to eliminate the division sign it becomes x^(-1) so when you do the integration process which is always add 1 to the exponent and divide the term by that answer, However when you add 1 to a -1 you get zero, and any term to the zero exponent = 1, so that’s why the natural log comes in. In the first integral above = ln(x), then you can enter the ranges for x that you are given, do the top range first and subtract the bottom range to get the answer (area under the curve of the function). The second integral above you’d break it into two integrals ∫[1/(c+b)] dx which equals x/(c+b) and then the second term 1/[(k+x)]dx which equals ln(k+x). 

I’m really trying to figure out how to use your program with a couple different problem examples: 

“Find the following derivatives of f(x). Do not leave any negative exponents”

1. F(x)= 4^x-ln(2x^2-x)

What program can I use to solve this?

another is f(x)=2csc(x)+5arccos(x)

This is fundamental to calculus and you must start to learn it or know it.

Notice the minus sign between the terms (if a plus no difference)

This means that the derivatives of the terms are separate or individual

You differentiate each by itself and one at a time

There could be 15 more terms each separated by a minus or plus and you’d do each one separate.

So:   f(x) =  4^x f’(x) =  x*4^(x-1)  Notice when differentiating you take the exponent

Multiply it times the front of the term and take one away from the exponent.

You must do this process in your sleep and fast or you’ll have trouble passing calculus

Another Example

f(x) = 15x^7

f ‘(x) = derivative

         = 7*15*x^(7-1)

         = 105x^6

Integration is the exact opposite

You add one to the exponent first

Then divide by that new exponent

∫[105*x^6] dx

= 6+1 = 7

So:   105*x^7 / 7

     = 15x^6

Problem 1) the trig problem

Reload the attached program

First Delete the same named program from you calculator

Then reload the attached changing to “Archives” first

For the problem go to:

“trig” in my menu

Scroll to csc(x)

Find the derivative and add the 2 in the front of the answer

For arcos(x)

Scroll to cos-1 in the menu of trig

And find that derivative adding the 5 in front

“Answer the following questions about the given function: f(x)=x^3-6x^2+9

A) Find f'(x)

B) Find f”(x)

These again are separated by minus and plus signs so each is differentiated separately

f(x) = x^3 – 6*x^2 + 9

f ’(x) = 3x^2 – 12x + 0

f ‘’ (x) = 6x – 12

Notice I took the exponent and multiplied it by the front of the term

And then took one away from the exponent in each case.

Do these in your sleep!!!!!

Use log differentiation to find the derivative of the following function with respect to variable x.

(x^3+2)^3sqrt(2x^2+3)

Notice the “times” sign so you’d be thinking “product rule” or logs to differentiate

First it must be expanded:

I have expanded log problems to another base

But haven’t programmed to expand natural logs, but am in the process.

Should be done soon

 (x^3+2)^3  *  √(2*x^2+3

ln((x^3+2)^3)  +  ln(√(2*x^2+3)   (always you change a square root to ^(1/2)

= ln( (x^3+2)^3 )  +  ln( (2*x^2+3)^(1/2) )

=  3*ln( x^3+2 )  + (1/2)*ln( 2*x^2+3 )

Now you can choose in my menu

“log Problems”

Choose “ln(x)”

Choose “differentiate”

And add the above ln tems one at a time

Put the problem back together when finished with the individual solutions.

Can the Calculus App do the Following?

F(x)=6x^-5

 F(x)= 6x^4-4x^3+5x^2

Answer:

f(x) = 6x^5    would be “derivative/algebra” for differentiation

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.

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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

 ..

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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

oh my god I figured it out. You’re the freaking best!      -Sarah

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

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Calculus Cheat Sheet Video Transcript

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