Hello. Tom from everystepcalculus.com and everystepphysics.com. Another Green’s theorem regarding a unit circle and its dividend. Index 8 get to my menu scroll down to Green’s theorem year what is the only reason that we’re studying this stuff is crap is to pass our calculus test passed her test that’s the only reason we have no interest in it whatsoever unit or going to work at NASA we have no interest in it keep that in mind raising our professors charity she disliked there are some basis for some goodness 40 are evergreen serum here problem from Yahoo gets have to press alpha beforehand or anything in these entry lines here is now four times why where the axe function and three times C looks pretty good reason to I say it’s ok they gave me MRP using MNE and here and it goes as the partials hebrew 3-6 unit circle convert to pull their situations circles Mexico said it takes our way it was caught sight of theater times are and we’re gonna do the first or detain Dr agreed defeated come up with minus six times over 250 compute that come up with minus 12 hi I mean agreed that Dr in a girl putting minor stroke pioneer over 10 subtract them and we come up with minus 12 high school career. Pretty neat, huh? everystepcalculus.com and everystephysics.com. Don’t do this step without my programs. Have a good one.
Hello everyone, Tom from everystepcalculus.com and everystepphysics.com. We’re talking about arc length today. Got this on a new test that somebody sent me so I’m going to do a video of it right now. Pretty complicated nonsense in calculus but still there for calculus two, people. So let’s do it, index 8, type in into the home screen there to get to my main menu. Your going to choose number 5, arc length and because the problem gives it an x, or a g a y. I’m going to choose number 2. And we’re going to, I show you the formula here, here’s the formula for the arc length and the x function given is, you have to press alpha before
you enter anything into my entry lines here. Alpha y cubed divided by 6 plus one divided by 2 times y. Looks good. I always show you which of entered, you can change it if you want. I say it’s good. I choose number 1, okay. I always show you the derivative first; take the derivative of that. I give you the choice of which system they give you too. If they give you y, then we’re cool in this system here. We just enter what they give you. If they entered x then you have to compute the y values that were given the X values. So we’re gonna do alpha 2 or, lower one is alpha 2, upper limit is alpha 3, or range, upper range. And I show you that also in case you made a mistake. I say it’s ok. We do our computations. This shows you the exact problem which is what you’re dealing with and what you write down in your paper, here. And we’re going to square that as part of the functions, here. You notice that calculus is so pathetic that they do one derivative and the rest of it is you have to do square roots, you have to do squares, you have to do integrals. Well, I do that all for you. Here’s squared. Now we’re going to add one to what we’ve squared which equals this, here. We’re going to take the square root of that whole mess right here. And we’re going to take the integral of that which is this right here. And over this range 3 and 2. Y equals 2, substitute that in for the original equation here and you get thirteen twelves, add 3 substitute that in, you get 13 over 3, you take the upper minus the lower and you come up with thirteen over 4 or 3.25 units. But pretty neat, huh? everystepcalculus.com. Go to my site and hope that I make other videos for you. Have a good one.
Hi, I’m Tom from everystepcalculus.com and everystepphysics.com. This is a linear approximation problem in calculus one generally because one variable and we’re going to read it here because it’s off of a test using your approximation to approximate square root of 49.4. We’re going to let f of X equals the square root of x and then that can be written as the point-slope form of y equals MX plus B so we’re going to compute m and B. Let’s do it, Index 8 to get to my menu. We’re going to scroll down here to linear approximation, in the L section. And we’re going to use one variable because there’s only x given. So linear approximation, one variable, I’m going to use the point-slope form equation for a tangent line to occur y equals MX plus B. We’re going to enter function, you have to press alpha before you enter anything into these entry lines here. So it’s alpa and second X will give us the square root sign put in the X close off the parentheses. Press Enter. I always show you what you’ve entered you can change it if you want. We’re going to enter the point but you want to evaluate this at. We’re going to press alpha again and I’m going to pull 49.4. Check that make sure it’s right again. I say it’s okay. First thing we do is we enter the function and get it do the derivative of that which is the slope and it equals m. Here’s the derivative of that. And we find that the closest square root number for that given number 49 and we add that into the derivative and so the slope is equal to one over 14. Now we take that number 49 again and add it into the original function. We came up with y equals seven. So the point is 49 for x and 7 y, okay. Y equals seven, then we’re going to find B so we do the calculations here in algebra. And b turns out to be 7 halves . We found that already, ok. If you want to go further and they’re asked for this point slope form this is equal to y equals MX plus B slope times X to speak now we’re going to enter the original point where after in the same formula and so then y is equal to 7.029, okay? And the XY is 49.4, 7.029. Pretty neat,huh? everystepcalculus.com. Go to my site, buy my programs, and pass calculus. Have a good one.