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  4. For m, n ∈ N, the value of displaystyle lim x arrow 0 ( sin xn/ sin xm) is equal to

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Q. For $m, n \in N$, the value of $\displaystyle\lim _{x \rightarrow 0} \frac{\sin x^{n}}{\sin x^{m}}$ is equal to

NTA AbhyasNTA Abhyas 2022

Solution:

Given $m, n \in N$
Now, $\displaystyle\lim _{x \rightarrow 0} \frac{\sin x^{n}}{\sin x^{m}}$
$=\displaystyle\lim _{x \rightarrow 0} \frac{\frac{\sin x^{n}}{x^{n}} x^{n}}{\frac{\sin x^{m}}{x} x^{m}} $
$=\displaystyle\lim _{x \rightarrow 0} x^{n-m}=0 \text { for } n>m$