Question

Evaluate the limit using L'Hospital's rule if necessary
limit ((9x)/(9x+3))^(7x)
x->inf

Answer 1

This one looks like a toughie.
First we can factor 3 out of the numerator and denominator:
((9x)/(9x+3))^(7x) = (3x/(3x+1))^(7x)
Let y = ((3x)/(3x+1))^(7x)
Take natural logarithm on both sides:
ln(y) = (7x) * ln(3x/(3x+1))
See if you can take the limit as x->infinity.
7 is a constant that can be factored out of the limit.

Answer 2

idk if this is right