Find the Maclaurin series for the function $$f ( x ) = \cos \left( x ^ { 17 / 2 } \right)$$
A) $\cos \left( x ^ { 17 / 2 } \right) = 1 - \frac { x ^ { 17 } } { 2 ! } + \frac { x ^ { 34 } } { 4 ! } - \cdots$
B) $\cos \left( x ^ { 17 / 2 } \right) = x - \frac { x ^ { 2 } } { 2 ! } + \frac { x ^ { 4 } } { 4 ! } - \cdots$
C) $\cos \left( x ^ { 17 / 2 } \right) = x + \frac { x ^ { 17 } } { 17 ! } + \frac { x ^ { 34 } } { 34 ! } + \cdots$
D) $\cos \left( x ^ { 17 / 2 } \right) = 1 + \frac { x ^ { 17 } } { 2 ! } + \frac { x ^ { 34 } } { 4 ! } + \cdots$
E) $\cos \left( x ^ { 17 / 2 } \right) = x - \frac { x ^ { 17 } } { 17 ! } + \frac { x ^ { 34 } } { 34 ! } - \cdots$

Question

Find the Maclaurin series for the function $$f ( x ) = \cos \left( x ^ { 17 / 2 } \right)$$ 
A) $\cos \left( x ^ { 17 / 2 } \right) = 1 - \frac { x ^ { 17 } } { 2 ! } + \frac { x ^ { 34 } } { 4 ! } - \cdots$
B) $\cos \left( x ^ { 17 / 2 } \right) = x - \frac { x ^ { 2 } } { 2 ! } + \frac { x ^ { 4 } } { 4 ! } - \cdots$
C) $\cos \left( x ^ { 17 / 2 } \right) = x + \frac { x ^ { 17 } } { 17 ! } + \frac { x ^ { 34 } } { 34 ! } + \cdots$
D) $\cos \left( x ^ { 17 / 2 } \right) = 1 + \frac { x ^ { 17 } } { 2 ! } + \frac { x ^ { 34 } } { 4 ! } + \cdots$
E) $\cos \left( x ^ { 17 / 2 } \right) = x - \frac { x ^ { 17 } } { 17 ! } + \frac { x ^ { 34 } } { 34 ! } - \cdots$

Quizplus · Accepted Answer

The Maclaurin series for $\cos(x)$ is $1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \cdots$. Substituting $x^{17/2}$ for $x$, we get $1 - \frac{(x^{17/2})^2}{2!} + \frac{(x^{17/2})^4}{4!} - \cdots$, which simplifies to $1 - \frac{x^{17}}{2!} + \frac{x^{34}}{4!} - \cdots$.

Find the Maclaurin Series for the Function f(x)=cos⁡(x17/2)f ( x ) = \cos \left( x ^ { 17 / 2 } \right)f(x)=cos(x17/2)

Find the Maclaurin Series for the Function $f ( x ) = \cos \left( x ^ { 17 / 2 } \right)$