We have, lim_x→ 0log cosx/x At x=0,the value of the expression is the form 0/0 applying L'Hospital Rule lim_x→ 0d ...

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Existence of Limit

lim x → 0logc...

Question

$lim x \to 0 \frac{l o g c o s x}{x} =$
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Solution

We have, $lim x \to 0 \frac{l o g c o s x}{x}$

At x=0,the value of the expression is the form $\frac{0}{0}$

applying L'Hospital Rule

$lim x \to 0 \frac{\frac{d}{d x} (l o g c o s x)}{\frac{d}{d x} x}$

= $lim x \to 0 \frac{\frac{1}{c o s x} . \frac{d}{d x} c o s x}{1}$

= $lim x \to 0 \frac{1}{c o s x} * (- s i n x)$

$lim x \to 0 - t a n x$

putting x=0

=-tan 0=0.

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