What is the limit as x approaches infinity of #xtan(1/x)#?

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Answer 1 · 2014-12-14T23:50:39

#lim_{x to infty}x tan(1/x)#

by #x=1/{1/x}#,

#=lim_{x to infty}{tan(1/x)}/{1/x}#

by l'H#hat{"o"}#pital'sRule (0/0),

#=lim_{x to infty}{sec^2(1/x)cdot(-1/x^2)}/{-1/x^2}#

by cancelling out #-1/x^2#,

#=lim_{x to infty}sec^2(1/x)=sec^2(1/infty)=sec^2(0)=1#

I hope that this was helpful.