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Consider the function f : R? → R defined by f(x, y) = x² – 3y (x,y E R) and the point a = (2, –2) e R². (1) Use the definition of continuity and the e – 8 argument to prove that f is continuous at a. (ii) Find the Jacobian matrix of f at a (iii) Use the definition of the differentiability and the e – 6 | argument to prove that f is differentiable at a.

Consider the function f : R? → R defined by f(x, y) = x² – 3y (x,y E R) and the point a = (2, –2) e R². (1) Use the definition of continuity and the e – 8 argument to prove that f is continuous at a. (ii) Find the Jacobian matrix of f at a (iii) Use the definition of the differentiability and the e – 6 | argument to prove that f is differentiable at a.

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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Consider the function f : R? → R defined by f(x, y) = x? – 3y (x, y E R) - and the point a = (2, –2) e R². (1) Use the definition of continuity and the e – 8 argument to prove that f is continuous at a. (ii) Find the Jacobian matrix of f at a (iii) Use the definition of the differentiability and the e – 8 argument to prove that f is differentiable at a.
Transcribed Image Text:Consider the function f : R? → R defined by f(x, y) = x? – 3y (x, y E R) - and the point a = (2, –2) e R². (1) Use the definition of continuity and the e – 8 argument to prove that f is continuous at a. (ii) Find the Jacobian matrix of f at a (iii) Use the definition of the differentiability and the e – 8 argument to prove that f is differentiable at a.
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