Finding the value of this limit $$\lim_{x\to 0}\frac{\sin x^4-x^4\cos x^4+x^{20}}{x^4(e^{2x^4}-1-2x^4)}$$
The answer is given to be $1$. Can someone give any hint/s related to this problem?
More importantly, why am I not able to get the answer by simply  using L hopital's rule and by basic substitution of trigonometric and exponential limits?
Any kind of help would be appreciated. I gave the problem simply as an example to reflect the above confusion.
EDIT: Even though tag says so, you are still allowed to use l hospital's rule to help evaluate the limit. 
The question is edited now. It is e^(2x^4) in denominator. 
Again, thanks a lot for taking your time to reply to my doubt. 

Divide numerator and denominator by $x^4$, giving you
$$\lim_{x\to 0}\frac{\frac{\sin x^4}{x^4}-\cos x^4+x^{16}}{e^{2x^4}-1-2x^4}$$
Now expand the sine, cosine, and exponential into power series (Maclaurin series) with as many terms as needed.
