How do you find the limit #lim_(x->0)tan(x)/x# ?

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Answer 1 · 2014-09-08T04:53:55

Answer
By using: #lim_{x to 0}{sinx}/{x}=1#, #lim_{x to 0}{tanx}/x=1#.

Explanation
Let us look at some details.
Since #tanx={sinx}/{cosx}#,

#lim_{x to 0}{tanx}/x = lim_{x to 0}{sinx}/{x}cdot1/{cosx}#

by the Product Rule,

#=(lim_{x to 0}{sinx}/x)cdot(lim_{x to 0}1/{cosx})#

by #lim_{x to 0}{sinx}/{x}=1#,

#=1cdot1/{cos(0)}=1#