What is taylor cos(x)e^x ?

The answer to taylor cos(x)e^x is 1+x-1/3 x^3-1/6 x^4-1/30 x^5+\ldots

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taylor cos(x)e^x

taylor

cos (x) e^{x}

1 + x - \frac{1}{3} x^{3} - \frac{1}{6} x^{4} - \frac{1}{30} x^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= 1 + x - \frac{1}{3} x^{3} - \frac{1}{6} x^{4} - \frac{1}{30} x^{5} + \dots

What is taylor cos(x)e^x ?
The answer to taylor cos(x)e^x is 1+x-1/3 x^3-1/6 x^4-1/30 x^5+\ldots