GATE 2025 MT – Question 52
The value of $\displaystyle\lim_{x\to0}\frac{6(x-\sin x)}{x^3}$ is ______ (in integer).
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Correct answer: 1 to 1
Explanation
Use $\sin x=x-x^3/6+O(x^5)$. Then $6(x-\sin x)=x^3+O(x^5)$.
Dividing by $x^3$ gives $1+O(x^2)$, which tends to **1**.