lim (cosx)^(1/x^2)
x-->0
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lim (cosx)^(1/x^2)
x-->0
Suggestion: if
Then
Now use de Moivre's theorem to find the limit of ln(L). Then L is e raised to that value.
A trick we can use is by observing thatfor
Now, make the sub:
and we get:
Notice, this looks mighty similar to the famous 'e' limit:
except we have a
Thus, the limit is
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