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Asked by Laura

Using L'Hospital's rule:
find, lim as x approaches (-) infinity of xsin(1/x)
16 years ago

Answers

Answered by drwls
Let u = 1/x.
The limit can then be written
lim as u -> 0 of (sin u)/u

Use L'Hopital's rule on that and you get (cos 0)/1 = 1.

I could have also taken the ratio of the derivatives of sin(1/x) and (1/x), but the other way was easier.
(-1/x^2)*cos (1/x)/(-1/x^2) = cos(1/x),
the limit of which as x -> infinity
is 1
16 years ago

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