Evaluate the limit- limx- 0sin 3x-sin xsin x

Lim_x→ 0sin 3x sin xsin x =lim_x→ 0sin 3x3x× 3x sin xx× xsin xx× x =lim_x→ 01× 3x 1 × x1 × x [∵lim_x→ 0sin xx=1] nbsp; = 2 Therefore, lim_x→ 0sin 3x si ...

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Standard XII

Mathematics

Algebra of Limits

Evaluate the ...

Question

Evaluate the limit:
$lim x \to 0 \frac{s i n 3 x - s i n x}{s i n x}$

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Solution

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

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

$= lim x \to 0 \frac{1 \times 3 x - 1 \times x}{1 \times x} [∵ lim x \to 0 \frac{s i n x}{x} = 1]$

$= 2$

Therefore,

$lim x \to 0 \frac{s i n 3 x - s i n x}{s i n x} = 2$

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Algebra of Limits

Standard XII Mathematics

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Evaluate the limit: limx→0sin 3x−sin xsin x

limx→0sin 3x−sin xsin x =limx→0sin 3x3x×3x−sin xx×xsin xx×x =limx→01×3x−1×x1×x [∵limx→0sin xx=1] =2 Therefore, limx→0sin 3x−sin xsin x=2

Evaluate the limit:
$lim x \to 0 \frac{s i n 3 x - s i n x}{s i n x}$