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1) Find ôz l ôu and ôzlôv for z= 4e* In(y), x= In(u cos(v)), y=u sin(v) at the point (u,v)=(2,7/4). Ans. z, = v2(In 2+2), z, =-2v2(In 2- 2) %3D %3D

1) Find ôz l ôu and ôzlôv for z= 4e* In(y), x= In(u cos(v)), y=u sin(v) at the point (u,v)=(2,7/4). Ans. z, = v2(In 2+2), z, =-2v2(In 2- 2) %3D %3D

Calculus: Early Transcendentals
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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1) Find ôz / ôu and ôzlôv for z= 4e" In(y), x= In(u cos(v)), y =usin(v) at the point (u,v)3(2,7/4). Ans. z, = 2(In 2+ 2), z, =-2/2(In 2-2) 2) Find ôw/ ôu and Ow/ôv for w=xy + yz + xz, x =u +v, y=u-v, z = uv at the point (u, v) = (1/2.1). 3 Ans. z, = 3, z, =- 2 50 Mathematics Second Year Electrical & Electronic Engineering Department Dr. Atheer Alaa Sabri 3) Find ôulÔx, ôu/ôy and ôu / ôz for u =- p-q p = x+y+z, q-r q = x- y+z, r = x+y-z at the point (x, y,z)=(V3,2,1) Ans. u, = 0, u, = 1, u =-2 4) Find ôw/or if w= (x+ y+ z), x =r-s, y= cos(r+s), z =sin(r + s) at the point (r,s)= (1,-1) Ans. 12 5) Find ôw/ov if w= x² +(y/x), x=u- 2v+1, and y = 2u + v- 2, at the point (u, v)= (0,0) Ans. -7 6) Find ôzlôu and ôzl ôv if z= 5 tan (x) and x= e" + In v at the point (u,v)= (In 2,1) Ans. z, = 2, z, = 1 Find dy/ dx at the given point for the following functions 1) x' -2y? + xy = 0, (1,1) Ans. 4/3 2) x* + xy + y -7=0, (1,2) Ans. -4/5 51
Transcribed Image Text:1) Find ôz / ôu and ôzlôv for z= 4e" In(y), x= In(u cos(v)), y =usin(v) at the point (u,v)3(2,7/4). Ans. z, = 2(In 2+ 2), z, =-2/2(In 2-2) 2) Find ôw/ ôu and Ow/ôv for w=xy + yz + xz, x =u +v, y=u-v, z = uv at the point (u, v) = (1/2.1). 3 Ans. z, = 3, z, =- 2 50 Mathematics Second Year Electrical & Electronic Engineering Department Dr. Atheer Alaa Sabri 3) Find ôulÔx, ôu/ôy and ôu / ôz for u =- p-q p = x+y+z, q-r q = x- y+z, r = x+y-z at the point (x, y,z)=(V3,2,1) Ans. u, = 0, u, = 1, u =-2 4) Find ôw/or if w= (x+ y+ z), x =r-s, y= cos(r+s), z =sin(r + s) at the point (r,s)= (1,-1) Ans. 12 5) Find ôw/ov if w= x² +(y/x), x=u- 2v+1, and y = 2u + v- 2, at the point (u, v)= (0,0) Ans. -7 6) Find ôzlôu and ôzl ôv if z= 5 tan (x) and x= e" + In v at the point (u,v)= (In 2,1) Ans. z, = 2, z, = 1 Find dy/ dx at the given point for the following functions 1) x' -2y? + xy = 0, (1,1) Ans. 4/3 2) x* + xy + y -7=0, (1,2) Ans. -4/5 51
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