4.7 Power Series A power series is an expression of the form 80 anxn = ao + a1 x + a2x² + an xn n=0 an terms is constant but x is averiable whose domain of real number. 1- if y = eax dny = . dxn yn where n-order derivative→ yn = an eax Example 1// if y = e²x find dy7 y7 27e2x=128e2x = = sin ax→ y = a” sin(ax + n Soltion/ 2. if y Example //if y = sin 3x find dy5 Solution //y5 = 35 sin (3x + 577) = 243 sin(3x + 5) π 3. if y = cos ax → y" = a" cos(ax + n −) 2

4.7 Power Series A power series is an expression of the form 80 anxn = ao + a1 x + a2x² + an xn n=0 an terms is constant but x is averiable whose domain of real number. 1- if y = eax dny = . dxn yn where n-order derivative→ yn = an eax Example 1// if y = e²x find dy7 y7 27e2x=128e2x = = sin ax→ y = a” sin(ax + n Soltion/ 2. if y Example //if y = sin 3x find dy5 Solution //y5 = 35 sin (3x + 577) = 243 sin(3x + 5) π 3. if y = cos ax → y" = a" cos(ax + n −) 2

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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