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Calculus

Limits, Standard Limits

jee_main_2026_april_2_shift_1

Grade 12

Question:

The value of lim_{x→0} (sin 3x)/(tan 5x) is:

A. 0

B. 3/5

C. 5/3

D. 1

Step-by-Step Solution

Key Concept: Use the standard limits: lim_{x→0} sin x/x = 1 and lim_{x→0} tan x/x = 1.

Step 1: lim_{x→0} (sin 3x)/(tan 5x) = lim_{x→0} [(sin 3x)/(3x) × (5x)/(tan 5x) × (3x)/(5x)]. Step 2: = 1 × 1 × 3/5 = 3/5.

Correct Answer: B

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