Solving for m: Find Limit of [e^(mx^2)-cos(8x)]/x^2 = 64

[sparkle123]

Find m:
lim([e^(mx^2)-cos(8x)]/x^2)=64 where x-->0

I used l'hopital's twice and got
lim [2m^2x^2e^(mx^2)+32cos(8x)]
=32

which means the limit is never 64.
the right answer is m=32 though. Where am I wrong?

 

[Sethric]

Redo the second derivative of your numerator. Especially the first term.

 

[sparkle123]

Got it! Thanks :)