What is taylor cos(4x) ?

The answer to taylor cos(4x) is 1-8x^2+32/3 x^4-256/45 x^6+512/315 x^8+\ldots

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taylor cos(4x)

taylor

cos (4 x)

1 - 8 x^{2} + \frac{32}{3} x^{4} - \frac{256}{45} x^{6} + \frac{512}{315} x^{8} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( cos ( 4 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( cos ( 4 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( cos ( 4 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- 16}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{256}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 4096}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{65536}{8 !} x^{8} + \dots

Refine

= 1 - 8 x^{2} + \frac{32}{3} x^{4} - \frac{256}{45} x^{6} + \frac{512}{315} x^{8} + \dots

csc (x) (x + cot (x))

e^{- x^{2}}

\int_{0}^{s i n (x)} 6 t d t

y^{^{''}} + 2 y^{^{'}} - 48 y = 0

\int \frac{u}{u} d u

What is taylor cos(4x) ?
The answer to taylor cos(4x) is 1-8x^2+32/3 x^4-256/45 x^6+512/315 x^8+\ldots