
# 6E: Review Excersies


## Exercise $$\PageIndex{1}$$

Evaluate the indicated limit or explain why it does not exist.

1) $$\displaystyle \lim_{(x,y)\to(0,0)} {2\sqrt{x^2+y^2}}$$

2) $$\displaystyle \lim_{(x,y)\to(0,0)} \frac{3x}{x^2+y^2}$$

3) $$\displaystyle \lim_{(x,y)\to(0,0)} \frac{2\sin(xy)}{x^2+y^2}$$

4) $$\displaystyle \lim_{(x,y)\to(0,0)} \frac{4x^2y^2}{x^2+y^4}$$

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## Exercise $$\PageIndex{2}$$

Define $$f(0,0)$$ in a way that extends \[f(x,y)=2xy \frac{x^2-y^2}{x^2+y^2}\[ to be continuous at the origin.

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## Exercise $$\PageIndex{3}$$

Find the first partial derivative of \[f(x,y,z)=3x^{(y\ln z)}\[ at $$(e,2,e)$$.