What is maclaurin e^{4x} ?

The answer to maclaurin e^{4x} is 1+4x+8x^2+32/3 x^3+32/3 x^4+\ldots

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maclaurin e^{4x}

maclaurin

e^{4 x}

1 + 4 x + 8 x^{2} + \frac{32}{3} x^{3} + \frac{32}{3} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( e ^{4 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{4 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{4 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{4}{1 !} x + \frac{16}{2 !} x^{2} + \frac{64}{3 !} x^{3} + \frac{256}{4 !} x^{4} + \dots

Refine

= 1 + 4 x + 8 x^{2} + \frac{32}{3} x^{3} + \frac{32}{3} x^{4} + \dots

\int \frac{cos ( ln ( 4 x ^{2} ) )}{x} d x

6 y^{^{'}} = y^{2}, y (0) = 5

(2 x - 1)^{^{'}}

\int \frac{x ^{2}}{( 4 - x ^{2} ) ^{\frac{3}{2}}} d x

y = e^{x} sin (x)

What is maclaurin e^{4x} ?
The answer to maclaurin e^{4x} is 1+4x+8x^2+32/3 x^3+32/3 x^4+\ldots