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Find dw/ dt at the given value for the following functions dw Ans. 1) w=x+y, x cos(t), y= sin(t), at t=t = 0 dt et dw 2) w =+,x = cos'(1),y sin (1), z=, at t = 3 Ans. = 1 dt 3 3) w=2 ye"-In(z), x In(r +1), y tan "(1),z e', dw = T +1 dt Ans. at t =1

Find dw/ dt at the given value for the following functions dw Ans. 1) w=x+y, x cos(t), y= sin(t), at t=t = 0 dt et dw 2) w =+,x = cos'(1),y sin (1), z=, at t = 3 Ans. = 1 dt 3 3) w=2 ye"-In(z), x In(r +1), y tan "(1),z e', dw = T +1 dt Ans. at t =1

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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2y -xcos xy 2y-xcos xy 49 Mathematics Second Year Electrical & Electronic Engineering Department Dr. Atheer Alaa Sabri Exercises Find dw/ dt at the given value for the following functions dw Ans. = 0 dt a 1) w= x +y, x= cos(t), y= sin(t), at t = dw Ans. dt y 1 2) w=*+,x= cos (t), y = sin (t),z =', at t = 3 = 1 dw = n +1 dt el 3) w= 2 ye" -In(z), x In(t +1), y= tan (t),z e', Ans. at t =1 Answer the following questions: 1) Find ôz l ôu and ôz/ôv for z= 4e' In(y), x = In(u cos(v)), y =u sin(v) at the point (u, v)3 (2,7/4). Ans. z, = /2(1In 2+2), z, =-22(In 2-2) 2) Find Ow/ Ou and ôw/dv for w= xy + yz + xz, x= u +v, y= u-v, z = uv at the point (u, v) = (1/2,1). Ans. z, = 3, z, 2 50 Mathematics Second Year Electrical & Electronic Engineering Department Dr. Atheer Alaa Sabri Find ôu / ôx, ôu / ôy and ôu / ôz for u= p-q p= x+y+z, 3) 9-r q =x-y+z, r =x+y-z at the point (x, y, z)= (V3,2,1)
Transcribed Image Text:2y -xcos xy 2y-xcos xy 49 Mathematics Second Year Electrical & Electronic Engineering Department Dr. Atheer Alaa Sabri Exercises Find dw/ dt at the given value for the following functions dw Ans. = 0 dt a 1) w= x +y, x= cos(t), y= sin(t), at t = dw Ans. dt y 1 2) w=*+,x= cos (t), y = sin (t),z =', at t = 3 = 1 dw = n +1 dt el 3) w= 2 ye" -In(z), x In(t +1), y= tan (t),z e', Ans. at t =1 Answer the following questions: 1) Find ôz l ôu and ôz/ôv for z= 4e' In(y), x = In(u cos(v)), y =u sin(v) at the point (u, v)3 (2,7/4). Ans. z, = /2(1In 2+2), z, =-22(In 2-2) 2) Find Ow/ Ou and ôw/dv for w= xy + yz + xz, x= u +v, y= u-v, z = uv at the point (u, v) = (1/2,1). Ans. z, = 3, z, 2 50 Mathematics Second Year Electrical & Electronic Engineering Department Dr. Atheer Alaa Sabri Find ôu / ôx, ôu / ôy and ôu / ôz for u= p-q p= x+y+z, 3) 9-r q =x-y+z, r =x+y-z at the point (x, y, z)= (V3,2,1)
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