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Calculus

Limits, Standard Limits

jee_main_2026_april_8_shift_1

Grade None

Question:

Find the value of lim_{x→0} (sin 6x - sin 4x)/(tan 5x).

A. 1/5

B. 2/5

C. 3/5

D. 4/5

Step-by-Step Solution

Key Concept: Use sin A - sin B = 2 cos((A+B)/2) sin((A-B)/2).

Step 1: sin 6x - sin 4x = 2 cos 5x sin x. Step 2: Expression = 2 cos 5x sin x / tan 5x. Step 3: As x→0, sin x/tan 5x ≈ x/(5x) = 1/5. Step 4: Limit = 2 cos 0 × 1/5 = 2 × 1 × 1/5 = 2/5.

Correct Answer: B

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