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

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sparkle123
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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?
 
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Redo the second derivative of your numerator. Especially the first term.