What is maclaurin 3cos(2x) ?

The answer to maclaurin 3cos(2x) is 3-6x^2+2x^4-4/15 x^6+2/105 x^8+\ldots

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maclaurin 3cos(2x)

maclaurin

3 cos (2 x)

3 - 6 x^{2} + 2 x^{4} - \frac{4}{15} x^{6} + \frac{2}{105} x^{8} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 3 + \frac{0}{1 !} x + \frac{- 12}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{48}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 192}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{768}{8 !} x^{8} + \dots

Refine

= 3 - 6 x^{2} + 2 x^{4} - \frac{4}{15} x^{6} + \frac{2}{105} x^{8} + \dots

x \to 2 lim (6 x - 2)

\int_{0}^{3} x + 1 d x

n = 0 \sum \infty \frac{9}{4} (\frac{1}{4})^{n}

tan (x), 3

\frac{\partial}{\partial x} (8 x y^{2} z^{3})

What is maclaurin 3cos(2x) ?
The answer to maclaurin 3cos(2x) is 3-6x^2+2x^4-4/15 x^6+2/105 x^8+\ldots