What is maclaurin e^{2x^2} ?

The answer to maclaurin e^{2x^2} is 1+2x^2+2x^4+4/3 x^6+2/3 x^8+\ldots

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maclaurin e^{2x^2}

maclaurin

e^{2 x^{2}}

1 + 2 x^{2} + 2 x^{4} + \frac{4}{3} x^{6} + \frac{2}{3} x^{8} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{4}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{48}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{960}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{26880}{8 !} x^{8} + \dots

Refine

= 1 + 2 x^{2} + 2 x^{4} + \frac{4}{3} x^{6} + \frac{2}{3} x^{8} + \dots

x \to \infty lim (\frac{7.5 x + 120000}{x})

\int \frac{4}{4 + e ^{4 x}} d x

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

\int θ sin (θ) cos (θ) d θ

\frac{\partial}{\partial x} ((7 x + 8 y)^{3})

What is maclaurin e^{2x^2} ?
The answer to maclaurin e^{2x^2} is 1+2x^2+2x^4+4/3 x^6+2/3 x^8+\ldots