GATE 2025 BM – Question 32
For $f(x)=x-1/x$, evaluate $\lim_{\Delta x\to0}[f(1+\Delta x)-f(1)]/\Delta x$.
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Correct answer: (D) 2
Explanation
The limit is the derivative f′(1). Differentiating gives f′(x)=1+1/x², hence f′(1)=2. Therefore D; the minus reciprocal term contributes a positive reciprocal-square derivative.