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 $lim_{x to 0}{sinx}/{x}=1$ ,

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

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