I understand how to use L'Hopitals rule for the most part but these two problems confuse me to no end. I would appreciate it if someone could show me how they are to be done.
first one...
limx→∞xe−x
second one...
limx→π2−tanxln(x2−x)
Answer
Gerry Myerson’s comment should take care of the first problem. The second one has to be misstated: I’ve very little doubt that it should be
limx→(π2)−tanxln(π2−x).
Corrected: If so, apply l’Hospital’s rule once and do a little simplification:
limx→(π2)−tanxln(π2−x)=limx→(π2)−sec2x−1π2−x=limx→(π2)−sec2x(x−π2)=limx→(π2)−x−π2cos2x.
Now apply l’Hospital’s rule one more time.
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