SOLUTION: Find the limit using l'Hospital's Rule. lim(as x approaches to 0+)13(x)e^(1/x)

Question 1201082: Find the limit using l'Hospital's Rule.
lim(as x approaches to 0+)13(x)e^(1/x)
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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Find the limit using l'Hospital's Rule.
lim(as x approaches to 0+)13(x)e^(1/x)
~~~~~~~~~~~~~~~~~~~~~~

Introduce new variable t = 1/x.


Then the function takes the form  g(t) = .


It is well known fact that the exponent    rises much faster than any polynomial;

therefore,  lim (as t --> oo)    = oo  (infinity).


It implies  that  lim (as x approaches to 0+)  of    is  oo  (infinity).    ANSWER

This proof is done without using the l'Hopital rule, simply using well known facts
from Calculus about the rate of rising of basic elementary functions.

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