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1. Consider a rectangle with length l and width w, both changing. (a) Show that Δ-w)- ( ) . w+. (Δω) + (Δ) (Δω) (Hint: draw a picture.) (b) Suppose / and w both change depending on some quantity x. Divide the above equation by Ax + 0 and rearrange to get A(I · w) Al w+1 Ax AL Aw Ax. Ax Ax Aw Ax Ax dw dl Hence show that if and exist (i.e. / and w are differentiable functions of x) then dx dx A(1 · w) dx d dw w+1. dx dl (I· w) dx lim Ax-0 Ax

1. Consider a rectangle with length l and width w, both changing. (a) Show that Δ-w)- ( ) . w+. (Δω) + (Δ) (Δω) (Hint: draw a picture.) (b) Suppose / and w both change depending on some quantity x. Divide the above equation by Ax + 0 and rearrange to get A(I · w) Al w+1 Ax AL Aw Ax. Ax Ax Aw Ax Ax dw dl Hence show that if and exist (i.e. / and w are differentiable functions of x) then dx dx A(1 · w) dx d dw w+1. dx dl (I· w) dx lim Ax-0 Ax

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. Consider a rectangle with length Il and width w, both changing. (a) Show that Δw) - (ΔΙ) . w+l. (Δω) + (Δ) (Δω). (Hint: draw a picture.) (b) Suppose ! and w both change depending on some quantity x. Divide the above equation by Ax + 0 and rearrange to get A(I - w) AL Aw Ax 'Ar Ax. A! Aw Ax •w+1. Ax Ar dw dl and dx Hence show that if exist (i.e. I and w are differentiable functions of x) then dx d A(1 - w) dl w+1. dx dw dr(1- w) lim Ax-0 Ax dx *
Transcribed Image Text:1. Consider a rectangle with length Il and width w, both changing. (a) Show that Δw) - (ΔΙ) . w+l. (Δω) + (Δ) (Δω). (Hint: draw a picture.) (b) Suppose ! and w both change depending on some quantity x. Divide the above equation by Ax + 0 and rearrange to get A(I - w) AL Aw Ax 'Ar Ax. A! Aw Ax •w+1. Ax Ar dw dl and dx Hence show that if exist (i.e. I and w are differentiable functions of x) then dx d A(1 - w) dl w+1. dx dw dr(1- w) lim Ax-0 Ax dx *
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