The Maclaurin series for f(x)=cos( $\sqrt{\x}$ )

asked by guest
on Nov 15, 2024 at 2:31 pm



You asked:

Find the Maclaurin series of the function f(x)=cos⁡(x)f\left( x \right) = \cos\left( \sqrt{x} \right).

MathBot Answer:

Series expansion:

1−x2+x224−x3720+x440320−x53628800+⋯1- \frac{x}{2} + \frac{x^{2}}{24}- \frac{x^{3}}{720} + \frac{x^{4}}{40320}- \frac{x^{5}}{3628800}+ \cdots

Series representation:

∑n=0∞(−1)nxn(2n)!\sum_{n=0}^{\infty} \frac{\left(-1\right)^{n} x^{n}}{\left(2 n\right)!}

Converges for all values of xx

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