Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. Problem with Linear Approximation in Calculus 3 with three variables in this video. Let’s do it. Index 8 to get my menu. Press second and the cursor here to go down screen by screen
and you get down to the L section where linear approximation is. Three variables.
Here’s the formula. W equals linear approximation equals the function of XYZ and a change in the function here is almost the same as the derivative a function. So here’s a derivative here. Write this stuff on your paper, of course. Alpha to put anything into the entry lines, here. We’re going to put their function in. Alpha They’re all square roots on these linear approximations. X squared plus Y squared well plus Z squared is the function.
Close of the parentheses. I always show you what you’ve entered, you can change it if you want. And you’re gonna put in, you can see the you can see in the example on the screen here.And so the Alpha, this is the points where you’re gonna approximate at. Alpha 1.97. Alpha 5.99 Again, I show you. The are the ABC’s, whole numbers of the fractions here. dx, dy, dz is these x minus a, and y minus b and z minus c which is this right here minus a
Here’s y, this 2 and z minus c. And then we have the derivative of w with respect to x.
w with respect to y, w with respect to z. Here’s how that turns out. And 3 2 6 equals .429. Partial y at 326 is . 286. Partial of z of 326is .857. And the actual function at326 is 7. So we’re gonna add these things together. In other words dx dy dz add together and then we
times the dx dy dz and dw equals .009. And 7 plus this equals 6.991. Pretty neat, huh? Try that without my program, try it by memory sometime with all the other nonsense of calculus. Have a good one. Subscribe to me and on my site you can more videos that you might like.