Let f(r,y) = Vr² + 2y². ) Compute the gradient of f at (1,2). 1. (a) / (b). Compute the tangent plane of f at (1, 2). (c) Use linear approximation to estimate the value of f(1.05, 1.9).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Could you please help me with a-c? Thank you!

Let f(r,y) = Vr² + 2y².
) Compute the gradient of f at (1,2).
1.
(a) /
(b).
Compute the tangent plane of f at (1, 2).
(c)
Use linear approximation to estimate the value of f(1.05, 1.9).
Transcribed Image Text:Let f(r,y) = Vr² + 2y². ) Compute the gradient of f at (1,2). 1. (a) / (b). Compute the tangent plane of f at (1, 2). (c) Use linear approximation to estimate the value of f(1.05, 1.9).
Expert Solution
Step 1

Part (a):

 

 

Consider the given function f(x, y)

 

The gradient is given as:

 

Advanced Math homework question answer, step 1, image 1

Step 2

part(b):

The tangent plane of function f (x,y) at (1,2):

Advanced Math homework question answer, step 2, image 1

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