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

The answer to taylor cos(x^2),0 is 1-1/2 x^4+1/24 x^8+\ldots

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taylor cos(x^2),0

taylor

cos (x^{2}), 0

1 - \frac{1}{2} x^{4} + \frac{1}{24} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 12}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{1680}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= 1 - \frac{1}{2} x^{4} + \frac{1}{24} x^{8} + \dots

x \to 1 lim (- 6)

x \to - π lim (cos (x + π) - 1)

\int \frac{1}{( 4 x ^{2} - 25 ) ^{2}} d x

x - 1, 2 x + 6, [- 2, 4]

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

What is taylor cos(x^2),0 ?
The answer to taylor cos(x^2),0 is 1-1/2 x^4+1/24 x^8+\ldots