Find the limit as x approaches 0 of (sin(ax)) / (sin(bx)) where b is not 0.

C. a/b — Multiply and divide by ax and bx respectively to use the standard limit sin(theta)/theta = 1 as theta approaches 0. This yields (ax * (sin(ax)/ax)) / (bx * (sin(bx)/bx)), which simplifies to a/b.

JEE Main · MathematicsMedium

$lim_{x \to 0} \frac{s i n ( a x )}{s i n ( b x )}$

A. $a$
B. $b$
C. $a/b$
D. $b/a$

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Correct answer: C — $a/b$

Solution

x \to 0 lim \frac{sin ( a x )}{a x} \cdot \frac{b x}{sin ( b x )} \cdot \frac{a x}{b x} = 1 \cdot 1 \cdot \frac{a}{b} = \frac{a}{b} .

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limx→0​sin(bx)sin(ax)​

Solution

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$lim_{x \to 0} \frac{s i n ( a x )}{s i n ( b x )}$