1. Consider the function f(r, y) = e=y. (a) Graph the level curves for this function for k = e, e?,e3, and e4 on the same graph to make a "topographical map" of the surface. Make a conjecture based on this graph what the surface looks like, in words. (b) Find the first and second partial derivatives of f. (c) Find an equation of the tangent plane of f(x, y) at the point (In 2, 3, 8). Use this to approximate the value of f(x, y) at (In 2 + 0.01, 3.02).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Kindly solve it as soon as possible with step by step approach. Kindly solve it's all parts a,b,c. Thankyou!!
1. Consider the function f(r, y) = ey.
(a) Graph the level curves for this function for k = e, e?, e3, and e on the
same graph to make a "topographical map" of the surface. Make a
conjecture based on this graph what the surface looks like, in words.
(b) Find the first and second partial derivatives of f.
(c) Find an equation of the tangent plane of f(x, y) at the point (In 2, 3, 8).
Use this to approximate the value of f(a, y) at (In 2 + 0.01,3.02).
Transcribed Image Text:1. Consider the function f(r, y) = ey. (a) Graph the level curves for this function for k = e, e?, e3, and e on the same graph to make a "topographical map" of the surface. Make a conjecture based on this graph what the surface looks like, in words. (b) Find the first and second partial derivatives of f. (c) Find an equation of the tangent plane of f(x, y) at the point (In 2, 3, 8). Use this to approximate the value of f(a, y) at (In 2 + 0.01,3.02).
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