11. Consider the function F: R² \{(0,0)} → R give by: F(x, y) = In(42² + y²) + e®¥y. (a) Find the partial derivatives of F, where they exist. (b) Find the gradient of F, where it exists. Find the largest open subset of R² where F is differentiable. Make sure to justify your answer (that is, make sure to explain what allows you to be sure that the function F is differentiable where you claim it to be).
11. Consider the function F: R² \{(0,0)} → R give by: F(x, y) = In(42² + y²) + e®¥y. (a) Find the partial derivatives of F, where they exist. (b) Find the gradient of F, where it exists. Find the largest open subset of R² where F is differentiable. Make sure to justify your answer (that is, make sure to explain what allows you to be sure that the function F is differentiable where you claim it to be).
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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Transcribed Image Text:11.
Consider the function F: R² \ {(0,0)}
→ R give by:
F(x, y) = In(4x² + y²) + e#Yy.
(a)
Find the partial derivatives of F, where they exist.
(b)
Find the gradient of F, where it exists.
Find the largest open subset of R2 where F is differentiable. Make sure to justify your
(c)
answer (that is, make sure to explain what allows you to be sure that the function F is differentiable
where you claim it to be).
(d)
the graph of F.
Find an equation for the tangent plane to the graph of F at the point (0, 1, F(0, 1)) on
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