The value of limx - 1 1 -xtan - x2 is

The correct option is A 2π We can write the above limit as, #160; lim_x→ 0(1 x)(π x2) .Substituting gives us indeterminate form.So, applying L'Hospi ...

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Standard XII

Mathematics

Substitution Method to Remove Indeterminate Form

The value of ...

Question

The value of $lim x \to 1 (1 - x) tan (\frac{π x}{2})$ is

\frac{π}{2}

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π + 2

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\frac{2}{π}

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none of these

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Solution

The correct option is A $\frac{2}{π}$
We can write the above limit as, ${lim}_{x \to 0} \frac{(1 - x)}{cot (\frac{π x}{2})}$ .
Substituting gives us indeterminate form.
So, applying L'Hospital's Rule,
$= {lim}_{x \to 0} \frac{- 1}{- {cosec}^{2} (\frac{π x}{2}) . \frac{π}{2}}$
$= \frac{- 2}{- π} = \frac{2}{π}$
Hence, option 'C' is correct.

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The value of limx→1(1−x)tan(πx2) is

The correct option is A 2πWe can write the above limit as, limx→0(1−x)cot(πx2).Substituting gives us indeterminate form.So, applying L'Hospital's Rule,=limx→0−1−cosec2(πx2).π2=−2−π=2πHence, option 'C' is correct.

The value of $lim x \to 1 (1 - x) tan (\frac{π x}{2})$ is