Use the relationship
$\displaystyle \int \frac{1}{\sqrt{1-x^2}}\ dx = \arcsin x + C$
to find the first four nonzero terms in the Maclaurin's series for $\displaystyle arcsinx$.
I don't have any idea on how to relate them together. thanks in advance.
Use the relationship
$\displaystyle \int \frac{1}{\sqrt{1-x^2}}\ dx = \arcsin x + C$
to find the first four nonzero terms in the Maclaurin's series for $\displaystyle arcsinx$.
I don't have any idea on how to relate them together. thanks in advance.
Hi
With the information you gave us, we know that
$\displaystyle f(x) = \arcsin(x) \ \\ f'(x) = \frac{1}{\sqrt{1-x^2}}$
A maclaurin series is
$\displaystyle f(x) = f(0) +f'(0)\frac{x^1}{1!}+f''(0)*\frac{x^2}{2!}+...+f^{ (n)}*\frac{x^{(n)}}{(n!)}$
so what we're missing now are $\displaystyle f''(x), f^{(3)}(x),$ etc. witch is up to you do find!
Remember you only have to find the first 4 that are non equal to 0.
Hope that helped, if not let me know!