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Walking on a surface Consider the following
Chapter 11, Problem 52E(choose chapter or problem)
Walking on a surface Consider the following surfaces specified in the form z = f(x, y) and the curve C in the xy-plane given parametrically in the form x = g(t), y = h(t).
a. In each case, find z'(t).
b. Imagine that you are walking on the surface directly above the curve C in the direction of increasing t. Find the values of 1 for which you are walking uphill (that is, z is increasing).
\(z=2 x^{2}+y^{2}+1, C: x=1+\cos t, y=\sin t ; 0 \leq t \leq 2 \pi\)
Questions & Answers
QUESTION:
Walking on a surface Consider the following surfaces specified in the form z = f(x, y) and the curve C in the xy-plane given parametrically in the form x = g(t), y = h(t).
a. In each case, find z'(t).
b. Imagine that you are walking on the surface directly above the curve C in the direction of increasing t. Find the values of 1 for which you are walking uphill (that is, z is increasing).
\(z=2 x^{2}+y^{2}+1, C: x=1+\cos t, y=\sin t ; 0 \leq t \leq 2 \pi\)
ANSWER:Solution 52EStep 1 of 4:In this problem we need to find the z'(t).Given: a. In each case, find z'(t).We have The chain rule for one independent variable states that,We have We have