John J.

asked • 07/20/17

Calculus Question

Evaluate the following limit:
 
Limit of xcotx as x approaches 0.

1 Expert Answer

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Arturo O. answered • 07/20/17

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Arturo O.

One way to solve this is to use L'Hopitla's rule.  Are you familiar with it?
 
limx→0 xcotx = limx→0 [(x cosx)/sinx] = limx→0 [(cosx - xsinx)/cosx] = limx→0 (1 - x tanx)] = 1
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07/20/17

Arturo O.

Another way to solve this is to use the following limit:
 
limx→0 (sinx/x) = 1
 
Then
 
limx→0 xcotx = limx→0 [x(cosx / sinx)] = limx→0 [cosx / (sinx / x)] = 1
 
In my previous comment I meant to say "L'Hopital's rule."
 
 
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07/20/17

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