What is taylor cos(pi-4x) ?

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

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taylor cos(pi-4x)

taylor

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

\int \frac{3}{125} x^{2} d x

x \to 0 lim (4 x)

\int (\frac{3}{x ^{2}} - \frac{2}{x ^{3}}) d x

n = 1 \sum \infty \frac{n !}{n \cdot 3 ^{n}}

y = 18 sin (x), y = 18 cos (x)

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