What is taylor cos(5x) ?

The answer to taylor cos(5x) is 1-25/2 x^2+625/24 x^4-3125/144 x^6+78125/8064 x^8+\ldots

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taylor cos(5x)

taylor

cos (5 x)

1 - \frac{25}{2} x^{2} + \frac{625}{24} x^{4} - \frac{3125}{144} x^{6} + \frac{78125}{8064} x^{8} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( cos ( 5 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( cos ( 5 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( cos ( 5 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- 25}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{625}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 15625}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{390625}{8 !} x^{8} + \dots

Refine

= 1 - \frac{25}{2} x^{2} + \frac{625}{24} x^{4} - \frac{3125}{144} x^{6} + \frac{78125}{8064} x^{8} + \dots

\int \frac{1}{2 x + 5} d x

x \to 0 lim (x + 3)

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

f^{^{'}} (t) = 0

\frac{d}{d x} ((x - 1)^{3})

What is taylor cos(5x) ?
The answer to taylor cos(5x) is 1-25/2 x^2+625/24 x^4-3125/144 x^6+78125/8064 x^8+\ldots