The correct option is C 2 lim _ x→Π /2 ( 2x Π #160; / cosx #160; ) ⇒ lim _ x→Π /2 2x Π =0 , ⇒ lim _ x→Π /2 cosx=0 lim _ x→Π /2 ( ...

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Derivative of Standard Functions

x →π2lim[ 2x-...

Question

$lim x \to \frac{π}{2} (\begin{matrix} \frac{2 x - π}{cos x} \end{matrix}) =$

0

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\frac{1}{2}

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- 2

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5

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Solution

The correct option is C $- 2$
${l i m}_{x \to Π / 2} (\frac{2 x - Π}{c o s x}) {\Rightarrow l i m}_{x \to Π / 2} 2 x - Π = 0, {\Rightarrow l i m}_{x \to Π / 2} c o s x = 0 {l i m}_{x \to Π / 2} (\frac{2 x - Π}{c o s x}) = \frac{0}{0} N o w u s i n g l^{'} h o s p i t a l^{'} s r u l e {l i m}_{x \to Π / 2} (\frac{2 x - Π}{c o s x}) = {l i m}_{x \to Π / 2} (\frac{\frac{d (2 x - Π)}{d x}}{\frac{d c o s x}{d x}}) = {l i m}_{x \to Π / 2} \frac{2}{- s i n x} = \frac{2}{- 1} = - 2$

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