Posted by Jane on .
5) Use the L’Hopital’s method to evaluate the following limits. In each case, indicate what type of limit it is ( 0/0, ∞/∞, or 0∙∞)
lim x→2 sin(x^2−4)/(x−2) =
lim x→+∞ ln(x−3)/(x−5) =
lim x→pi/4 (x−pi/4)tan(2x) =

L'Hopitals Rule 
Steve,
sin(x^24)/(x2) > 2xcos(x^24)/1 > 4
ln(x3)/(x5) > (1/(x3))/5 > 0
(xpi/4)tan(2x) = (xpi/4)/cot(2x) > 1/(2csc^2(2x)) = 1/2 sin^2(2x) > 1/2