How is the series relevant?

Calculus Level 3

If we know that the Maclaurin series of sin ( x 2 ) \sin(x^2) is

x 2 x 6 3 ! + x 10 5 ! x 14 7 ! + , x^2 - \dfrac{x^6}{3!} + \dfrac{x^{10}}{5!} - \dfrac{x^{14}}{7!} + \cdots ,

then what is the value of the 1 0 th 10^\text{th} derivative of sin ( x 2 ) \sin(x^2 ) at x = 0 x=0 ?

Notation : ! ! denotes the factorial notation. For example, 8 ! = 1 × 2 × 3 × × 8 8! = 1\times2\times3\times\cdots\times8 .

10 ! 5 ! \frac{10!}{5!} 10 ! 1 ! \frac{10!}{1!} 10 ! 7 ! \frac{10!}{7!} 10 ! 3 ! \frac{10!}{3!}

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

0 solutions

No explanations have been posted yet. Check back later!

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...