What is taylor cos(x)-x^2 ?

The answer to taylor cos(x)-x^2 is 1-3/2 x^2+1/24 x^4-1/720 x^6+1/40320 x^8+\ldots

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taylor cos(x)-x^2

taylor

cos (x) - x^{2}

1 - \frac{3}{2} x^{2} + \frac{1}{24} x^{4} - \frac{1}{720} x^{6} + \frac{1}{40320} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= 1 - \frac{3}{2} x^{2} + \frac{1}{24} x^{4} - \frac{1}{720} x^{6} + \frac{1}{40320} x^{8} + \dots

x \to 0 lim (6 sin (x) ln (x))

y = ln (a x a + x)

\frac{d}{d x} (arccos (- 2 x))

\frac{d}{d x} (\frac{x ^{2} + 4 x ^{\frac{1}{2}}}{x ^{2}})

sin (2 π t)

What is taylor cos(x)-x^2 ?
The answer to taylor cos(x)-x^2 is 1-3/2 x^2+1/24 x^4-1/720 x^6+1/40320 x^8+\ldots