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1. Draw the level curves corresponding to the values k = -4,-2, 0, 2, 4 for the function

f(x, y) = 2x² - y²

Lots of Limits (11.2)

2. Why does the limit of f(x, y) = 2xe" + xy sin(xy) exist for all values of x and y?

√xz6

4z

3. Why does the limit of f(x, y, z) = 2x sin(yz) + y² cos(x) —

z?

¹Special Thanks to Maya O. for helping me to put this together!

exist for all values of x, y, and/n4. What are a few things to look for when determining if a limit does or does not exist?

5. When proving that the limit of a function exists, what Calc. I theorem should we probably use?

6. For each of the following does the limit exist? Justify your answer. If it exists, find the limit.

cos(2x - y)

x² + y²

(a) lim

(z,y) (1.2)

(b)

(c) lim

(d)

xy²

lim

(z,y)+(0,0) 2x² + 2y²

(z,y) →(0,0)

sin(x² + y²)

x² + y²

xy²

lim

(z,y)+(0,0) 2x² + y²¹

Partial and Directional Derivatives (11.3-11.6)

7. Let z(s, t) = f(x(s, t), u(s, t)), where f. r. and u are differentiable functions. Suppose values for

Fig: 1

Fig: 2