1) f(x, y) = y-x. (2,1) Ans. Vf =-i+j 8(x, y) = y-x'. (-1,0) 3) f(x, y,z) = x +y-2z+z In(x), Ans. Vg 2i+j Ans. Vf 3i+ 2j-4k (1,1.1)

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 of the function at the given point
1) f(x, y) y-x, (2,1)
Ans. Vf =-i+j
2) 8(x, y) = y-x'. (-1,0)
3) f(x, y, z) = x +y - 2z° +z In(x).
Ans. Vg = 2i+j
Ans. Vf = 3i+ 2j- 4k
(1,1.1)
4) f(x, y, z) = (x² + y° +z°)"² + In(xyz),
23
Ans. Vf = - i+j-k
27
26
23,
(-1,2,-2)
54
54
Transcribed Image Text:Find the gradient of the function at the given point 1) f(x, y) y-x, (2,1) Ans. Vf =-i+j 2) 8(x, y) = y-x'. (-1,0) 3) f(x, y, z) = x +y - 2z° +z In(x). Ans. Vg = 2i+j Ans. Vf = 3i+ 2j- 4k (1,1.1) 4) f(x, y, z) = (x² + y° +z°)"² + In(xyz), 23 Ans. Vf = - i+j-k 27 26 23, (-1,2,-2) 54 54
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