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Q7 (10 points)
(Part A is worth 5 points; Part B is worth 5 points)
Leave numbers in generic form such as: $e^$, $\ln( )$, $\sqrt{*}$, etc., if applicable. No decimal numbers.
Part A. If $\displaystyle f(t) = 5\sqrt{t} – \frac{1}{t}$ for $t>0$ and $g(x,y) = x^2+y^2-5$, determine where $(f \circ g) (x,y)$ is continuous.
Part B. Given that $z=y^3 \sin(4x) + (x+x^2)^{\cos(x)}e^{-x^4} + \cos(3x) \arctan(y^2+1) \ln(y^3+42)$, find $\displaystyle \frac{\partial^2 f}{\partial x \partial y} $ when $x=\pi$ and $y=0$.
You must clearly and coherently justify your work – show your steps in your calculation. You cannot provide only the final answer. Circle your final answer for each part.

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