What is taylor e^{-x}0.25 ?

The answer to taylor e^{-x}0.25 is 0.25-0.25x+0.125x^2-0.04166…x^3+0.01041…x^4+\ldots

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taylor e^{-x}0.25

taylor

e^{- x} 0.25

0.25 - 0.25 x + 0.125 x^{2} - 0.04166 \dots x^{3} + 0.01041 \dots x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 0.25 + \frac{\frac{d}{d x} ( e ^{- x} \cdot 0.25 ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{- x} \cdot 0.25 ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{- x} \cdot 0.25 ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0.25 + \frac{- 0.25}{1 !} x + \frac{0.25}{2 !} x^{2} + \frac{- 0.25}{3 !} x^{3} + \frac{0.25}{4 !} x^{4} + \dots

Refine

= 0.25 - 0.25 x + 0.125 x^{2} - 0.04166 \dots x^{3} + 0.01041 \dots x^{4} + \dots

f (x) = 1 - 2 x^{2}, - 7, at x = 2

f (x) = 5 x - 4 x, at x = 1

y = \frac{1}{5 + 2 x}, (2, \frac{1}{9})

\frac{y ^{^{'}} - e ^{- t} + 4}{y} = - 4, y (0) = - 4

What is taylor e^{-x}0.25 ?
The answer to taylor e^{-x}0.25 is 0.25-0.25x+0.125x^2-0.04166…x^3+0.01041…x^4+\ldots