Lim x - 05 x-4 sin 3 x-4 sin 2 x-7 x

Lim_x→ 05x+4sin3x/4sin2x+7x =lim_x→ 05+4sin3x/x/4sin2x/x+7=lim_x→ 05+4lim_x→ 0sin3x/3x× 3/4lim_x→ 0sin2x/2x× 2+7 =5+4× 1 × 3/4 × 2+7=5+12/8+7=17/15 ...

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Byju's Answer

Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

lim x → 05 x+...

Question

${lim}_{x \to 0} \frac{5 x + 4 s i n 3 x}{4 s i n 2 x + 7 x}$

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Solution

${lim}_{x \to 0} \frac{5 x + 4 s i n 3 x}{4 s i n 2 x + 7 x}$

$= {lim}_{x \to 0} \frac{5 + \frac{4 s i n 3 x}{x}}{\frac{4 s i n 2 x}{x} + 7} = \frac{{lim}_{x \to 0} 5 + 4 {lim}_{x \to 0} \frac{s i n 3 x}{3 x} \times 3}{4 {lim}_{x \to 0} \frac{s i n 2 x}{2 x} \times 2 + 7}$

$= \frac{5 + 4 \times 1 \times 3}{4 \times 2 + 7} = \frac{5 + 12}{8 + 7} = \frac{17}{15}$

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limx→05x+4sin3x4sin2x+7x

limx→05x+4sin3x4sin2x+7x =limx→05+4sin3xx4sin2xx+7=limx→05+4limx→0sin3x3x×34limx→0sin2x2x×2+7 =5+4×1×34×2+7=5+128+7=1715

${lim}_{x \to 0} \frac{5 x + 4 s i n 3 x}{4 s i n 2 x + 7 x}$