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

The answer to maclaurin 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

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

maclaurin

\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 Maclaurin 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 (\frac{k}{2018}) x^{2} d x

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

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

\int \frac{1}{8 x + 2 x ^{2}} d x

x \to 2 lim (2 x^{2} + \frac{a}{2} x - 4)

What is maclaurin 1/2 (e^x+e^{-x}) ?
The answer to maclaurin 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