en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

taylor e^x,1

Solution

taylor

e^{x}, 1

Solution

n = 0 \sum \infty \frac{e ( x - 1 ) ^{n}}{n !}

Solution steps

Apply the Taylor Formula

= 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

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

The series sum representation

= n = 0 \sum \infty \frac{e ( x - 1 ) ^{n}}{n !}

Popular Examples

sum from n=0 to infinity of-n/(2^n)

n = 0 \sum \infty - \frac{n}{2 ^{n}}

area x^4-2x^2,2x^2 area

x^{4} - 2 x^{2}, 2 x^{2}

limit as x approaches infinity of x^n

x \to \infty lim (x^{n})

integral of cos^5(θ)sin(2θ)

\int cos^{5} (θ) sin (2 θ) d θ

integral of (x^2)/(1-x^2)

\int \frac{x ^{2}}{1 - x ^{2}} d x

Frequently Asked Questions (FAQ)

What is taylor e^x,1 ?
The answer to taylor e^x,1 is sum from n=0 to infinity of (e(x-1)^n)/(n!)