I understand how to do this problem up until the last simplification line. I was hoping you could explain a little further what happened here. Thanks Expand the function p (z + h) as follows.1p (z + h) =-1Substitute the function p (z + h) in equation (1).(w+h)2 –1= lim¬0h(w²–1)-/(w+h)²-1= lim½¬0h/(w+h)²-1(w²–1)(V(w2-1)-/(w+h)²–1)(/)-/(w+h)°-(w²–1= lim½¬0V(w+h)²–1–1)(/(w²-1)-/(w+h)° -w2-w2.w? –1-(w²+2wh+h² –1)= limh→0(w+h)?–i1)(/(w²-1)-/(w+h)²–1w2-1w2.Simplify the Equation.w?-1-(w²+2wh+h?–1)Z =lim-0h/(w+h)°-1 /(w²-1)(/(w2 – 1)-/(w+h)²–1v².-2w-h= limh¬0h/(w+h)° -1/(w²-1)((w?-1)-/(w+h)° -1w2–(w²–1)Thus, the derivative of the function vis(w²-1) ½ *

They are solving derivative for v=1w2-1

Expand the function p (z + h) as follows. p (z + h) = V(w+h)²–1 Substitute the function p (z + h) in equation (1). (w+h)2 –1 p = limh¬0 h (w²_ /(w+h)² –1 limh¬0 = h/(w+h)²_1 (w² –1) (w²–1)-/(w+h)²–1)(/ (w²- (w+h)? – -1 = limh¬0 h/(w+h)²–1\/ (w²–1) (w²–1)-/(w+h)²–1 w²–1-(w²+2wh+h?–1) = lim½¬0 h/(w+h)²_1. (w²–1)( /(w²-1)-V(w+h)²=1 Simplify the Equation. w² –1-(w²+2wh+h²–1) z = limh¬0 h/(w+h²-1 /[w²-1)(/(w²-1)-/(w+h²-1 (w2_j = lim½¬0 -2w-h (w2 –1)( /(w2 –1 2-1)-/(w+h)²– (w²–1) 3/½ Thus, the derivative of the function vis (w²-1) ½

Expand the function p (z + h) as follows. p (z + h) = V(w+h)²–1 Substitute the function p (z + h) in equation (1). (w+h)2 –1 p = limh¬0 h (w²_ /(w+h)² –1 limh¬0 = h/(w+h)²_1 (w² –1) (w²–1)-/(w+h)²–1)(/ (w²- (w+h)? – -1 = limh¬0 h/(w+h)²–1\/ (w²–1) (w²–1)-/(w+h)²–1 w²–1-(w²+2wh+h?–1) = lim½¬0 h/(w+h)²_1. (w²–1)( /(w²-1)-V(w+h)²=1 Simplify the Equation. w² –1-(w²+2wh+h²–1) z = limh¬0 h/(w+h²-1 /[w²-1)(/(w²-1)-/(w+h²-1 (w2_j = lim½¬0 -2w-h (w2 –1)( /(w2 –1 2-1)-/(w+h)²– (w²–1) 3/½ Thus, the derivative of the function vis (w²-1) ½

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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