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Consider the surface z=f(x,y)=x+3y +1 and the curve C in the xy-plane given parametrically as x = cost and y = sint where 0 st≤ 2. a. Find z' (t). b. Imagine that you are walking on the surface directly above the curve C in the direction of positive orientation. Find the values of + for which you are walking unbill that is is increasingl

Consider the surface z=f(x,y)=x+3y +1 and the curve C in the xy-plane given parametrically as x = cost and y = sint where 0 st≤ 2. a. Find z' (t). b. Imagine that you are walking on the surface directly above the curve C in the direction of positive orientation. Find the values of + for which you are walking unbill that is is increasingl

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the surface z = f(x,y) = x² + 3y² + 1 and the curve C in the xy-plane given parametrically as x = cost and y = sint where 0 st≤2. a. Find z' (t). b. Imagine that you are walking on the surface directly above the curve C in the direction of positive orientation. Find the values of t for which you are walking uphill (that is, z is increasing). a. Find the intermediate derivatives. əz ax (Type an expression using x and y as the variables.)
Transcribed Image Text:Consider the surface z = f(x,y) = x² + 3y² + 1 and the curve C in the xy-plane given parametrically as x = cost and y = sint where 0 st≤2. a. Find z' (t). b. Imagine that you are walking on the surface directly above the curve C in the direction of positive orientation. Find the values of t for which you are walking uphill (that is, z is increasing). a. Find the intermediate derivatives. əz ax (Type an expression using x and y as the variables.)
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