What is taylor cos^2(2θ) ?

The answer to taylor cos^2(2θ) is 1-4θ^2+16/3 θ^4-128/45 θ^6+256/315 θ^8+\ldots

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taylor cos^2(2θ)

taylor

cos^{2} (2 θ)

1 - 4 θ^{2} + \frac{16}{3} θ^{4} - \frac{128}{45} θ^{6} + \frac{256}{315} θ^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} θ + \frac{- 8}{2 !} θ^{2} + \frac{0}{3 !} θ^{3} + \frac{128}{4 !} θ^{4} + \frac{0}{5 !} θ^{5} + \frac{- 2048}{6 !} θ^{6} + \frac{0}{7 !} θ^{7} + \frac{32768}{8 !} θ^{8} + \dots

Refine

= 1 - 4 θ^{2} + \frac{16}{3} θ^{4} - \frac{128}{45} θ^{6} + \frac{256}{315} θ^{8} + \dots

y^{^{'}} = - 10 y, y (0) = 5

2 y^{^{''}} + y^{^{'}} - y = x + 7

x \to - \infty lim (x \cdot 0)

\int_{- 1}^{0} t^{\frac{1}{3}} - t^{\frac{2}{3}} d t

f (x) = - \frac{1}{4} x^{2}, (- 2, - 1)

What is taylor cos^2(2θ) ?
The answer to taylor cos^2(2θ) is 1-4θ^2+16/3 θ^4-128/45 θ^6+256/315 θ^8+\ldots