Calculus Archive: Questions from April 11, 2023
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If \( f(x, y)=x \sin (y / x) \), find \( \left(\right. \) a \( f(2, \pi / 2),(b) f_{x}(2, \pi / 2),(c) f_{y}(2, \pi / 2),(d) f_{x x}(2, \pi / 2),(e) f_{x y}(2, \pi / 2) \), \( (f) f_{y x}(2, \pi / 2),
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Evaluate the triple integral
E
f(x, y, z) dV
over the solid E.
f(x, y, z) = e√x2 + y2, E = {(x, y, z) | 1 ≤ x2 + y2 ≤ 4, y ≤
0, x ≤ y
3
, 7 ≤ z ≤ 8}
Evaluate the triple integral \( \iint_{E} f(x, y, z) d V \) over the solid \( E \). \[ f(x, y, z)=e^{\sqrt{x^{2}}+y^{2}}, E=\left\{(x, y, z) \mid 1 \leq x^{2}+y^{2} \leq 4, y \leq 0, x \leq y \sqrt{3}
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