What is taylor 1/2 (e^x+e^{-x}) ?

The answer to taylor 1/2 (e^x+e^{-x}) is 1+1/2 x^2+1/24 x^4+1/720 x^6+1/40320 x^8+\ldots

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

taylor 1/2 (e^x+e^{-x})

taylor

\frac{1}{2} (e^{x} + e^{- x})

1 + \frac{1}{2} x^{2} + \frac{1}{24} x^{4} + \frac{1}{720} x^{6} + \frac{1}{40320} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= 1 + \frac{1}{2} x^{2} + \frac{1}{24} x^{4} + \frac{1}{720} x^{6} + \frac{1}{40320} x^{8} + \dots

\int 4 8 - 3 x d x

12 arctan (s)

\int_{1}^{2} \frac{2}{( x - 5 ) ^{3}} d x

\int 4^{x} - \frac{1}{3 x} d x

8 (ln (y)) y^{^{'}} - x^{9} y = 0

What is taylor 1/2 (e^x+e^{-x}) ?
The answer to taylor 1/2 (e^x+e^{-x}) is 1+1/2 x^2+1/24 x^4+1/720 x^6+1/40320 x^8+\ldots