What is taylor e^{((-x^2))/4} ?

The answer to taylor e^{((-x^2))/4} is 1-1/4 x^2+1/32 x^4-1/384 x^6+1/6144 x^8+\ldots

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

taylor e^{((-x^2))/4}

taylor

e^{\frac{( - x ^{2} )}{4}}

1 - \frac{1}{4} x^{2} + \frac{1}{32} x^{4} - \frac{1}{384} x^{6} + \frac{1}{6144} x^{8} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( e ^{\frac{- x ^{2}}{4}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{\frac{- x ^{2}}{4}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{\frac{- x ^{2}}{4}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- \frac{1}{2}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{\frac{3}{4}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- \frac{15}{8}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{\frac{105}{16}}{8 !} x^{8} + \dots

Refine

= 1 - \frac{1}{4} x^{2} + \frac{1}{32} x^{4} - \frac{1}{384} x^{6} + \frac{1}{6144} x^{8} + \dots

n = 1 \sum \infty \frac{1}{n} + \frac{1}{n ^{2}}

\int \frac{x ^{2} + 4}{x} d x

x \to \infty lim (ln (x))

\int \frac{1}{x 12 x + 49} d x

\int \frac{1}{( 324 + x ^{2} ) ^{\frac{3}{2}}} d x

What is taylor e^{((-x^2))/4} ?
The answer to taylor e^{((-x^2))/4} is 1-1/4 x^2+1/32 x^4-1/384 x^6+1/6144 x^8+\ldots