What is maclaurin (cos(2x))/3 ?

The answer to maclaurin (cos(2x))/3 is 1/3-2/3 x^2+2/9 x^4-4/135 x^6+2/945 x^8+\ldots

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maclaurin (cos(2x))/3

maclaurin

\frac{cos ( 2 x )}{3}

\frac{1}{3} - \frac{2}{3} x^{2} + \frac{2}{9} x^{4} - \frac{4}{135} x^{6} + \frac{2}{945} x^{8} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= \frac{1}{3} + \frac{0}{1 !} x + \frac{- \frac{4}{3}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{\frac{16}{3}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- \frac{64}{3}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{\frac{256}{3}}{8 !} x^{8} + \dots

Refine

= \frac{1}{3} - \frac{2}{3} x^{2} + \frac{2}{9} x^{4} - \frac{4}{135} x^{6} + \frac{2}{945} x^{8} + \dots

y^{^{'}} - t y^{3} = 0, y (0) = 2

\int sin (t) tan (t) d t

14 x (x^{2} + 4)^{6}

5 x^{2} cos (x) cot (x)

What is maclaurin (cos(2x))/3 ?
The answer to maclaurin (cos(2x))/3 is 1/3-2/3 x^2+2/9 x^4-4/135 x^6+2/945 x^8+\ldots