Lim_x→π/4sin [ 2 ( x π/4 ) ]/ ( x π/4 ) ( 0/0form ) = lim_x→π/42cos [ 2 ( x π/4 ) ]/1=2 ...

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Standard Limits to Remove Indeterminate Form

limx→π/4sin2 ...

Question

${lim}_{x \to \frac{π}{4}} \frac{s i n 2 (x - \frac{π}{4})}{x - \frac{π}{4}}$ =

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\frac{1}{2}

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Solution

The correct option is D 2
${lim}_{x \to \frac{π}{4}} \frac{s i n [2 (x - \frac{π}{4})]}{(x - \frac{π}{4})} (\frac{0}{0} f o r m)$

$= {lim}_{x \to \frac{π}{4}} \frac{2 c o s [2 (x - \frac{π}{4})]}{1} = 2$

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