For constant n, evaluate x0 n(5x)/(3x).

GATE 2024 MN – Question 17

Engineering Mathematics · Calculus · 1 mark · Multiple choice

For constant n, evaluate $\lim_{x\to0} n\sin(5x)/\sin(3x)$.

2n
3n/5
6n/5
5n/3

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Show answer and explanation

Correct answer: (D) 5n/3

Explanation

Near zero, sin(5x)/(5x) and sin(3x)/(3x) both tend to 1. Their ratio therefore leaves the factor 5/3. Multiplying by n gives 5n/3, D. The coefficient n is not an exponent.

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