Lim x - 0sin 3 x-sin x-sin x

Lim_x→ 0sin3x sinx/sinx =lim_x→ 02cos ( 3x+x/x )sin ( 3x x/x )/sinx [Applying Componendo amp; dividendo formula] =lim_x→ 0 ( 2cos2xsinx/sinx ) =lim_x→ 0(2cos ...

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Byju's Answer

Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

lim x → 0sin ...

Question

${lim}_{x \to 0} \frac{s i n 3 x - s i n x}{s i n x}$

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Solution

${lim}_{x \to 0} \frac{s i n 3 x - s i n x}{s i n x}$

$= {lim}_{x \to 0} \frac{2 c o s (\frac{3 x + x}{x}) s i n (\frac{3 x - x}{x})}{s i n x}$

[Applying Componendo & dividendo formula]

$= {lim}_{x \to 0} (\frac{2 c o s 2 x s i n x}{s i n x})$

$= {lim}_{x \to 0} (2 c o s 2 x) = 2 {lim}_{x \to 0} c o s 2 x$

$= 2 \times c o s 0$

$= 2 \times 1 = 2$

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limx→0sin3x−sinxsinx

limx→0sin3x−sinxsinx =limx→02cos(3x+xx)sin(3x−xx)sinx [Applying Componendo & dividendo formula] =limx→0(2cos2xsinxsinx) =limx→0(2cos2x)=2limx→0cos2x =2×cos 0 =2×1=2

${lim}_{x \to 0} \frac{s i n 3 x - s i n x}{s i n x}$