What is taylor 1-cos(θ) ?

The answer to taylor 1-cos(θ) is 1/2 θ^2-1/24 θ^4+1/720 θ^6-1/40320 θ^8+1/3628800 θ^{10}+\ldots

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taylor 1-cos(θ)

taylor

1 - cos (θ)

\frac{1}{2} θ^{2} - \frac{1}{24} θ^{4} + \frac{1}{720} θ^{6} - \frac{1}{40320} θ^{8} + \frac{1}{3628800} θ^{10} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} θ + \frac{1}{2 !} θ^{2} + \frac{0}{3 !} θ^{3} + \frac{- 1}{4 !} θ^{4} + \frac{0}{5 !} θ^{5} + \frac{1}{6 !} θ^{6} + \frac{0}{7 !} θ^{7} + \frac{- 1}{8 !} θ^{8} + \frac{0}{9 !} θ^{9} + \frac{1}{10 !} θ^{10} + \dots

Refine

= \frac{1}{2} θ^{2} - \frac{1}{24} θ^{4} + \frac{1}{720} θ^{6} - \frac{1}{40320} θ^{8} + \frac{1}{3628800} θ^{10} + \dots

x \to - 1 lim (- x^{5} - 3 x^{4})

\int 16 x - x^{2} d x

\int_{- 1}^{3} x^{5} d x

\frac{1}{x - 1}, 2

\frac{d}{d x} (in (3 x + 1) (x + 2) 2)

What is taylor 1-cos(θ) ?
The answer to taylor 1-cos(θ) is 1/2 θ^2-1/24 θ^4+1/720 θ^6-1/40320 θ^8+1/3628800 θ^{10}+\ldots