The correct option is D 2/π lim_x→ 1(1 x)tan(π x2) =lim _ x→ 1 1 x (π x 2 #160; ) It is of the form 00 , so applying L Hospital's rul ...

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Substitution Method to Remove Indeterminate Form

limx→ 11-xtan...

Question

$lim x \to 1 (1 - x) tan (\frac{π x}{2}) =$

π

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2 π

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\frac{π}{2}

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\frac{2}{π}

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Solution

The correct option is D $\frac{2}{π}$
$lim x \to 1 (1 - x) tan (\frac{π x}{2})$
$= {lim}_{x \to 1} \frac{1 - x}{cot (\frac{π x}{2})}$
It is of the form $\frac{0}{0}$ , so applying L-Hospital's rule
$= {lim}_{x \to 1} \frac{- 1}{- \frac{π}{2} {csc}^{2} (\frac{π x}{2})}$
$= \frac{2}{π}$

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