What is maclaurin e^{3x} ?

The answer to maclaurin e^{3x} is 1+3x+9/2 x^2+9/2 x^3+27/8 x^4+\ldots

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maclaurin e^{3x}

maclaurin

e^{3 x}

1 + 3 x + \frac{9}{2} x^{2} + \frac{9}{2} x^{3} + \frac{27}{8} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{3}{1 !} x + \frac{9}{2 !} x^{2} + \frac{27}{3 !} x^{3} + \frac{81}{4 !} x^{4} + \dots

Refine

= 1 + 3 x + \frac{9}{2} x^{2} + \frac{9}{2} x^{3} + \frac{27}{8} x^{4} + \dots

\frac{\partial}{\partial x} (2 x e^{x y^{3}})

36 - y^{2}

y^{^{''}} - 5 y^{^{'}} + 6 y = cos (2 x) + 1

x \to + (- 1) - lim (2)

\frac{d}{d x} (- \frac{2 sec ^{2} ( x )}{( 1 + tan ( x ) ) ^{3}})

What is maclaurin e^{3x} ?
The answer to maclaurin e^{3x} is 1+3x+9/2 x^2+9/2 x^3+27/8 x^4+\ldots