Sunday, 19 January 2014

calculus - Can someone show how to find the limits of these functions using L'Hopitals rule?



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...



limxxex




second one...



limxπ2tanxln(x2x)


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(π2x).



Corrected: If so, apply l’Hospital’s rule once and do a little simplification:




limx(π2)tanxln(π2x)=limx(π2)sec2x1π2x=limx(π2)sec2x(xπ2)=limx(π2)xπ2cos2x.



Now apply l’Hospital’s rule one more time.


No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find limh0sin(ha)h without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...