I am studying for an entrance exam and would like somebody to confirm my answer or point out mistakes I made. Answers are greatly appreciated!
Find a and b so that the following Limit exists. $ L = \lim_{x\rightarrow 0} \frac{\cos^5{x} + ax + b}{x^2} $
My solution approach was using l'Hôpital's rule so I set a to 0 and b to -1. -1 cancels the 1 from cos 0 so I get 0/0 then I can use l'Hôpital's rule. Having a = 0 I can use it again.
Is this approach right?