Find the gradient vector and level curve of the following functions at the given point and show that the gradient is perpendicular to the level curve through the point.a) f(x,y) = x; (2,3)b) f(x,y) = x2+y2; (2,1)c) f(x,y) = x2-y; (2,1)I've already found the gradient vectors and level curves of all of them and also know that to be perpendicular to each-other, their dot product have to be zero, but I cannot find out how to prove that the dot product is zero.Thank you!

Answered: Find the gradient vector and level…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Find the gradient vector and level curve of the following functions at the given point and show that the gradient is perpendicular to the level curve through the point.

a) f(x,y) = x; (2,3)

b) f(x,y) = x²+y²; (2,1)

c) f(x,y) = x²-y; (2,1)

I've already found the gradient vectors and level curves of all of them and also know that to be perpendicular to each-other, their dot product have to be zero, but I cannot find out how to prove that the dot product is zero.

Thank you!

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