How do you find #lim (3+u^(-1/2)+u^-1)/(2+4u^(-1/2))# as #u->0^+# using l'Hospital's Rule?
l"Hospital's Rule is neither needed nor helpful for this limit.
We do get the indeterminate form
Therefore, we will continue to get the indeterminate
We no longer get an indeterminate form, so we cannot use (and have no need for) l'Hospital's Rule.
(The numerator is going to a positive limit and the denominator is going to