Multivariable Cal Practice Quiz 3.pdf - Multivariable...

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Multivariable Calculus Practical Quiz #3 by Dr. Jing, Berkshire School (2020 ~2021) Name_______________ Score___________ 1) Evaluate the limit or show that it does not exist. 2
2) Find all second partial derivatives.
3) Find equations of the tangent plane and the normal line to the given surface at the specific point.
4) Find the points on the hyperboloid where the tangent plane is parallel to the y x 2 + 4 2 z 2 = 4
5) Find du if n (1 e ) u = l + s 2 6) Find the linear approximation of the function at the point (2,3,4) and use it ( x , , ) f y z = x 3 y 2 + z t 2 3
7) If y , where x p p , y and z sinp , use the Chain Rule to find du / dp . u = x 2 3 + z 4 = + 3 2 = e p = p
8) If ( x ), where f is differentiable , show that z = y + f 2 y z /∂ x z /∂ y x y + x = 9) The length x of a side of a triangle is increasing at a rate of 3 in/s, the length y of another side is decreasing at a rate of 2 in/s, and the contained angle is increasing at a rate of 0.05 radian/s. 2 θ

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