You can put this solution on YOUR website! .
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.
