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

The answer to taylor e^{-x^2}cos(x) is 1-3/2 x^2+25/24 x^4-331/720 x^6+1979/13440 x^8+\ldots

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taylor e^{-x^2}cos(x)

taylor

e^{- x^{2}} cos (x)

1 - \frac{3}{2} x^{2} + \frac{25}{24} x^{4} - \frac{331}{720} x^{6} + \frac{1979}{13440} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- 3}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{25}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 331}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{5937}{8 !} x^{8} + \dots

Refine

= 1 - \frac{3}{2} x^{2} + \frac{25}{24} x^{4} - \frac{331}{720} x^{6} + \frac{1979}{13440} x^{8} + \dots

\int e^{2 x} \cdot sin (3 x) d x

\frac{d}{d x} (csc^{4} (x))

\frac{d}{d x} (\frac{e ^{2 x}}{x})

n = 0 \sum \infty \frac{5}{n !}

\frac{d}{d x} (\frac{1}{x ^{2} + 9})

What is taylor e^{-x^2}cos(x) ?
The answer to taylor e^{-x^2}cos(x) is 1-3/2 x^2+25/24 x^4-331/720 x^6+1979/13440 x^8+\ldots