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

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

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

taylor

\frac{e ^{x} + e ^{- x}}{2}

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

x \to 0 + lim (e^{2 + l n (x)})

x \to 7 - lim (f (x))

n = - \infty \sum \infty 1

n = 0 \sum \infty e^{- n}

arctan (\frac{3 + t}{3 - t})

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