GATE 2025 ES – Question 34
Evaluate $\lim_{x\to0}\ln(1+x)/(2\sin x)$,to two decimal places.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.50 to 0.50
Explanation
Factor the ratio as $\frac12[\ln(1+x)/x][x/\sin x]$. Both bracketed factors tend to 1 as x tends to zero, so the limit is **0.50**. Equivalently, L’Hôpital gives $(1/(1+x))/(2\cos x)$ evaluated at zero, also 1/2.