What is taylor 1/2 cos(7x) ?

The answer to taylor 1/2 cos(7x) is 1/2-49/4 x^2+2401/48 x^4-117649/1440 x^6+823543/11520 x^8+\ldots

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taylor 1/2 cos(7x)

taylor

\frac{1}{2} cos (7 x)

\frac{1}{2} - \frac{49}{4} x^{2} + \frac{2401}{48} x^{4} - \frac{117649}{1440} x^{6} + \frac{823543}{11520} x^{8} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{2} + \frac{\frac{d}{d x} ( \frac{1}{2} cos ( 7 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{2} cos ( 7 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{2} cos ( 7 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{2} + \frac{0}{1 !} x + \frac{- \frac{49}{2}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{\frac{2401}{2}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- \frac{117649}{2}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{\frac{5764801}{2}}{8 !} x^{8} + \dots

Refine

= \frac{1}{2} - \frac{49}{4} x^{2} + \frac{2401}{48} x^{4} - \frac{117649}{1440} x^{6} + \frac{823543}{11520} x^{8} + \dots

\frac{d y}{d x} = y^{2} + 2 y

\frac{d}{d x} (arccot (5 x^{2}))

\frac{\partial}{\partial x} (e^{i x})

y^{^{'}} + y = t

\frac{d}{d x} (\frac{x}{x + 3})

What is taylor 1/2 cos(7x) ?
The answer to taylor 1/2 cos(7x) is 1/2-49/4 x^2+2401/48 x^4-117649/1440 x^6+823543/11520 x^8+\ldots