What is taylor cos^2(x),0 ?

The answer to taylor cos^2(x),0 is 1-x^2+1/3 x^4-2/45 x^6+1/315 x^8+\ldots

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taylor cos^2(x),0

taylor

cos^{2} (x), 0

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{8}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 32}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{128}{8 !} x^{8} + \dots

Refine

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

sin (x) + \frac{4}{9} cot (x)

\int_{1}^{t} \frac{17}{x ^{3}} d x

3 - \frac{1}{2} x, 3 \leq x \leq 15

\int_{0}^{2} (x + 2 - x^{2}) d x

e^{x} + e^{- x}

What is taylor cos^2(x),0 ?
The answer to taylor cos^2(x),0 is 1-x^2+1/3 x^4-2/45 x^6+1/315 x^8+\ldots