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1. Let f: R²R where f(x, y) = x² + y² and c = (2, 2). (a) Find and simplify Df(c). (b) Find and simplify f(c)+L((x, y) — c). (c) What is the equation of the tangent plane to the graph of z = x² + y2 through the point (2,2, f(c))?

1. Let f: R²R where f(x, y) = x² + y² and c = (2, 2). (a) Find and simplify Df(c). (b) Find and simplify f(c)+L((x, y) — c). (c) What is the equation of the tangent plane to the graph of z = x² + y2 through the point (2,2, f(c))?

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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Real Analysis II
1. Let f: R²R where f(x, y) = x² + y² and c = (2, 2). (a) Find and simplify Df(c). (b) Find and simplify f(c) + L((x, y) — c). = (c) What is the equation of the tangent plane to the graph of z x² + y² through the point (2, 2, f(c))?
Transcribed Image Text:1. Let f: R²R where f(x, y) = x² + y² and c = (2, 2). (a) Find and simplify Df(c). (b) Find and simplify f(c) + L((x, y) — c). = (c) What is the equation of the tangent plane to the graph of z x² + y² through the point (2, 2, f(c))?
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