calculus limit question: another difficult limit problem I have posted previously on a problem in a similar vein here:
Limit evaluation: very tough question, cannot use L'hopitals rule
I believe this problem is very similar, but it has stumped me.
$$\lim_{x \to 0}\frac{1-\frac12 x^2 - \cos\left(\frac{x}{1-x^2}\right)}{x^4}$$
Really appreciate it if someone has some insight on this.This comes out to be indeterminate if one plugs in zero.
Following the idea from the link above, I tried to recognize this as derivative evaluated at zero of a function, BUT I could not find the function, because I tried to make this all over x, so that means the function I would create would generate a rational type with x^3 on the bottom.
I guess I should also try to look at some trig limit identities as well.
Hope someone out there can see how to navigate this problem.
P

$\frac 1{1-x^2}=1+x^2+O(x^4)$
 then $\frac x{1-x^2}=x+x^3+O(x^5)$
 then $\cos\left(\frac x{1-x^2}\right)=1-\frac{x^2}{2}-x^4+\frac{x^4}{24}+O(x^5)=1-\frac{x^2}{2}-\frac{23x^4}{24}+O(x^5)$ the limit is $\frac{23}{24}$.
