What is maclaurin e^x*sin(2x) ?

The answer to maclaurin e^x*sin(2x) is 2x+2x^2-1/3 x^3-x^4-19/60 x^5+\ldots

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maclaurin e^x*sin(2x)

maclaurin

e^{x} \cdot sin (2 x)

2 x + 2 x^{2} - \frac{1}{3} x^{3} - x^{4} - \frac{19}{60} x^{5} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{2}{1 !} x + \frac{4}{2 !} x^{2} + \frac{- 2}{3 !} x^{3} + \frac{- 24}{4 !} x^{4} + \frac{- 38}{5 !} x^{5} + \dots

Refine

= 2 x + 2 x^{2} - \frac{1}{3} x^{3} - x^{4} - \frac{19}{60} x^{5} + \dots

f (t) = t^{2} + 6 t - 3

f (x) = 2 x^{4}, (- 2, 32)

\int \frac{x + 3}{x ^{2} - 1} d x

\frac{d}{d x} (18 x e^{x^{2}})

t^{2} y^{^{''}} - 2 y = 3 t^{2} - 1, y (1) = \frac{3}{2}, y^{^{'}} (1) = 3

What is maclaurin e^x*sin(2x) ?
The answer to maclaurin e^x*sin(2x) is 2x+2x^2-1/3 x^3-x^4-19/60 x^5+\ldots