What is maclaurin 3sin(-2x^2) ?

The answer to maclaurin 3sin(-2x^2) is -6x^2+4x^6-4/5 x^{10}+\ldots

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maclaurin 3sin(-2x^2)

maclaurin

3 sin (- 2 x^{2})

- 6 x^{2} + 4 x^{6} - \frac{4}{5} x^{10} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{- 12}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{2880}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{- 2903040}{10 !} x^{10} + \dots

Refine

= - 6 x^{2} + 4 x^{6} - \frac{4}{5} x^{10} + \dots

x \to 0 lim ((1 + 2 x)^{\frac{1}{2 x ^{2}}})

\frac{d}{d x} (2 sin^{3} (x))

\int_{- 2}^{3} x^{2} - 4 d x

\int \frac{- 3}{y} d y

18 e^{t}

What is maclaurin 3sin(-2x^2) ?
The answer to maclaurin 3sin(-2x^2) is -6x^2+4x^6-4/5 x^{10}+\ldots