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NTA Abhyas JEE Main2020MathematicsLimitsPractice

For m , n ∈ N , the value of lim x → 0 ⁡ sin ⁡ x n sin ⁡ x m is equal to

Options

A1 , if n < m
B0 , if n = m
Cn m
D0 , if n > m

Correct answer

D. 0 , if n > m

Step-by-step solution

Given m , n ∈ N Now, lim x → 0 ⁡ sin ⁡ x n sin ⁡ x m = lim x → 0 ⁡ sin ⁡ x n x n x n sin ⁡ x x m x m = lim x → 0 ⁡ x n - m = 0 for n > m

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