We have, lim_x→ 1log x/x 1 At x=0,the value of the expression is the form 0/0 applying L'Hospital Rule lim_x→ 1d/dxlog x ...

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Indeterminate Forms

lim x → 1log ...

Question

$lim x \to 1 \frac{l o g x}{x - 1}$
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Solution

We have, $lim x \to 1 \frac{l o g x}{x - 1}$

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

applying L'Hospital Rule

$lim x \to 1 \frac{\frac{d}{d x} l o g x}{\frac{d}{d x} (x - 1)}$

$lim x \to 1 \frac{\frac{1}{x}}{1}$ ${\frac{d}{d x} l o g x = \frac{1}{x}}$

Putting x=1

= $\frac{1}{1} = 1$

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