What is taylor e^x,-1 ?

The answer to taylor e^x,-1 is 1/e+1/e (x+1)+1/(2e)(x+1)^2+1/(6e)(x+1)^3+1/(24e)(x+1)^4+\ldots

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

taylor e^x,-1

taylor

e^{x}, - 1

\frac{1}{e} + \frac{1}{e} (x + 1) + \frac{1}{2 e} (x + 1)^{2} + \frac{1}{6 e} (x + 1)^{3} + \frac{1}{24 e} (x + 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{e} + \frac{\frac{d}{d x} ( e ^{x} ) ( - 1 )}{1 !} (x + 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{x} ) ( - 1 )}{2 !} (x + 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{x} ) ( - 1 )}{3 !} (x + 1)^{3} + \dots

Evaluate Derivatives

= \frac{1}{e} + \frac{\frac{1}{e}}{1 !} (x + 1) + \frac{\frac{1}{e}}{2 !} (x + 1)^{2} + \frac{\frac{1}{e}}{3 !} (x + 1)^{3} + \frac{\frac{1}{e}}{4 !} (x + 1)^{4} + \dots

Refine

= \frac{1}{e} + \frac{1}{e} (x + 1) + \frac{1}{2 e} (x + 1)^{2} + \frac{1}{6 e} (x + 1)^{3} + \frac{1}{24 e} (x + 1)^{4} + \dots

What is taylor e^x,-1 ?
The answer to taylor e^x,-1 is 1/e+1/e (x+1)+1/(2e)(x+1)^2+1/(6e)(x+1)^3+1/(24e)(x+1)^4+\ldots