We are asked to find the Maclaurin series for a function involving
cos(x)
. Recall the Maclaurin series for
cos(x)
.
cos(x)=\sum_(n=0)^(\infty ) (-1)^(n)(x^(2n))/((2n)!)
The same equality would be true for any variable, and in particular for
u=(1)/(14)x^(2)
. Therefore, the Maclaurin series for
cos((1)/(14)x^(2))
is
\sum_(n=0)^(\infty ) (-1)^(n)((x)^(2n))/((2n)!)=\sum_(n=0)^(\infty ) (-1)^(n)(x^(4n))/((2n)!)

Question

We are asked to find the Maclaurin series for a function involving

cos(x)

. Recall the Maclaurin series for

cos(x)

.

cos(x)=\sum_(n=0)^(\infty ) (-1)^(n)(x^(2n))/((2n)!)

The same equality would be true for any variable, and in particular for

u=(1)/(14)x^(2)

. Therefore, the Maclaurin series for

cos((1)/(14)x^(2))

is

\sum_(n=0)^(\infty ) (-1)^(n)((x)^(2n))/((2n)!)=\sum_(n=0)^(\infty ) (-1)^(n)(x^(4n))/((2n)!)

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