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Use a CAS to perform the following steps for each of the functions.a. Plot the surface over the given rectangle.b. Plot several level curves in the rectangle.c. Plot the level curve of $f$ through the given point.$$\begin{aligned}&f(x, y)=\sin (x+2 \cos y), \quad-2 \pi \leq x \leq 2 \pi\\&-2 \pi \leq y \leq 2 \pi, \quad P(\pi, \pi)\end{aligned}$$

$$-2 \pi \leq x \leq 2 \pi,-2 \pi \leq y \leq 2 \pi$$$$f(x, y)$$$$P(f(x, y)=\sin 2)$$

Calculus 3

Chapter 14

Partial Derivatives

Section 1

Functions of Several Variables

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Lectures

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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Use a CAS to perform the f…

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In this problem were going to plot the given function, plot its level curves and also plot the little curve at the given point before i show you the graph that i've plotted- let's first figure out the equation for part c. So, to do that, we first need to evaluate the function at the given point. What it gives us is sine of pi plus 2 times cosine of pi and cosine of pi is negative 1. So we have a sine of pi minus 2 using the difference formula or the sign function. We can explain this to do sine pi times, cosine of 2 minus cosine of pi times sine of 2 point in of piero. So this is 0, so we have minus negative 1 times sine of t o t at the point. Pi pi or function is equal to positive sine of 2 point. So the equation for the level curve. At the point it would be sine of x, plus 2. Cosine y is equal to sine up 2 point, so this will be the equation that we're plotting in part. So i used the non line through the graph as well as there's mal sotoelevel curves. So here we have on the left the graph of function on the graph of the surface and on the right. I have a few level curves here and i have them for values of z equals negative 0.9 negative, 0.5, 0.5. And finally, here we have a little curve that goes to the point: pi 5.

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