What is taylor e^{-13x} ?

The answer to taylor e^{-13x} is 1-13x+169/2 x^2-2197/6 x^3+28561/24 x^4+\ldots

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taylor e^{-13x}

taylor

e^{- 13 x}

1 - 13 x + \frac{169}{2} x^{2} - \frac{2197}{6} x^{3} + \frac{28561}{24} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( e ^{- 13 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{- 13 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{- 13 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- 13}{1 !} x + \frac{169}{2 !} x^{2} + \frac{- 2197}{3 !} x^{3} + \frac{28561}{4 !} x^{4} + \dots

Refine

= 1 - 13 x + \frac{169}{2} x^{2} - \frac{2197}{6} x^{3} + \frac{28561}{24} x^{4} + \dots

\frac{d y}{d x} = \frac{( x ^{2} - 3 y ^{2} )}{2 x y}

\frac{\partial}{\partial x} (\frac{4 s + t}{3 s - 5 t})

y^{^{''}} + 49 y = 0, y (0) = 4, y^{^{''}} (0) = 6

\int_{0}^{1} x sin (x) d x

x \to - 1 lim (\frac{2 x + 8}{x})

What is taylor e^{-13x} ?
The answer to taylor e^{-13x} is 1-13x+169/2 x^2-2197/6 x^3+28561/24 x^4+\ldots