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Consider the function z = f(r, y) = ay e", a > 1 is a parameter. %3D %3D i. Find the gradient vector to f(r, y) at (r, y) = (0, 1). ii. Plot the gradient večtor from (i.) in the (x, y)-plane. In what direction is it pointing and what does this mean? iii. Calculate f(0,1). iv. Calculate the tangent plane to f(r, y) at (r, y) = (1,0).

Consider the function z = f(r, y) = ay e", a > 1 is a parameter. %3D %3D i. Find the gradient vector to f(r, y) at (r, y) = (0, 1). ii. Plot the gradient večtor from (i.) in the (x, y)-plane. In what direction is it pointing and what does this mean? iii. Calculate f(0,1). iv. Calculate the tangent plane to f(r, y) at (r, y) = (1,0).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 76E
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Study Resourcesv Textbook Solutions Expe Consider the function z = f(r, y) = ay e"", a > 1 is a parameter. i. Find the gradient vector to f(r, y) at (r, y) = (0, 1). ii. Plot the gradient vector from (i.) in the (x, y)-plane. In what direction is it pointing and what does this mean? iii. Calculate f(0,1). iv. Calculate the tangent plane to f(r, y) at (r, y) = (1,0). Consider the function 22 fix, 3) 2 eggs (191is a parameter. i Find the gradient vector to f(ry) at (say) 2 [011). i. Plot the gradient vector from (L) in the (ry)-plane. In 1What direction is it pointing and what does this mean? i. Calculate fa), 1). iv. Calculate the tangent plane to flay) at (my) 2 (1,0). t vecior to at ( .). eut vector from () in the -plane. In is it pointing and what does this mean? tangent plane to f(r) at (u) (1.0). 1 ques Ask a dus ECON 1540 17 80 888 DII DD F3 F4 F5 F6 F7 FB F9 F10 & 3 4 6 7 8 R T Y
Transcribed Image Text:Study Resourcesv Textbook Solutions Expe Consider the function z = f(r, y) = ay e"", a > 1 is a parameter. i. Find the gradient vector to f(r, y) at (r, y) = (0, 1). ii. Plot the gradient vector from (i.) in the (x, y)-plane. In what direction is it pointing and what does this mean? iii. Calculate f(0,1). iv. Calculate the tangent plane to f(r, y) at (r, y) = (1,0). Consider the function 22 fix, 3) 2 eggs (191is a parameter. i Find the gradient vector to f(ry) at (say) 2 [011). i. Plot the gradient vector from (L) in the (ry)-plane. In 1What direction is it pointing and what does this mean? i. Calculate fa), 1). iv. Calculate the tangent plane to flay) at (my) 2 (1,0). t vecior to at ( .). eut vector from () in the -plane. In is it pointing and what does this mean? tangent plane to f(r) at (u) (1.0). 1 ques Ask a dus ECON 1540 17 80 888 DII DD F3 F4 F5 F6 F7 FB F9 F10 & 3 4 6 7 8 R T Y
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