The correct option is C 1We have, lim_x→ 1log x/x 1 At x=1, the limit is of the form 0/0 i.e. indeterminate. Applying L'Hospital's rule, lim_x→ 1log x/x 1 = li ...

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Standard XI

Mathematics

Indeterminate Forms

lim x → 1log ...

Question

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

0.0

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\frac{1}{2}

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Solution

The correct option is C 1
We have, $lim x \to 1 \frac{l o g x}{x - 1}$
At x=1, the limit is of the form $\frac{0}{0}$ i.e. indeterminate.

Applying L'Hospital's rule,
$lim x \to 1 \frac{l o g x}{x - 1} = lim x \to 1 \frac{\frac{d}{d x} (l o g x)}{\frac{d}{d x} (x - 1)} = lim x \to 1 \frac{1}{x} = 1$

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limx→1log xx−1=

The correct option is C 1We have, limx→1log xx−1 At x=1, the limit is of the form 00 i.e. indeterminate. Applying L'Hospital's rule, limx→1log xx−1=limx→1ddx(log x)ddx(x−1)=limx→11x=1

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