SOLUTION: Evaluate the following limits by using the L'Hopital's Theorem a. lim as x approaches to positive infinity (2^x)/(e^(x^2))

Question 908637: Evaluate the following limits by using the L'Hopital's Theorem
a. lim as x approaches to positive infinity (2^x)/(e^(x^2))
Found 2 solutions by rothauserc, solver91311:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
a) f(x) = 2^x and g(x) = e^(x^2)
f'(x) = 2^x * log(2)
g'(x) = 2e^(x^2)x
then lim as x approaches infinity is 2^x * log(2) / (2e^(x^2)x = L
we see that lim as x approaches infinity of g(x) is +infinity which satisfies L'Hopital's Theorem criteria and
lim as x approaches infinity is 2^x * log(2) / (2e^(x^2)x = 1
b) lim as x approaches to 0 (sinx)^lncosx is 1

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The problem cannot be solved using L'Hopital because every derivative of contains a factor of and therefore increases without bound as increases without bound. Likewise, every derivative of contains a factor of and therefore increases without bound as increases without bound.

John

My calculator said it, I believe it, that settles it

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