Previous Year NEET Question- Limits

1. 2015

• Question: Evaluate $\lim_{x \to \infty} \frac{2x^2 - 3x + 1}{x^2 - 1}$
• Answer: 2

Explanation:

We can factor the numerator and denominator as follows:

$$\begin{align*} \lim_{x \to \infty} \frac{2x^2 - 3x + 1}{x^2 - 1} &= \lim_{x \to \infty} \frac{(2x - 1)(x - 1)}{(x + 1)(x - 1)} \ &= \lim_{x \to \infty} \frac{2x - 1}{x + 1} \ &= 2 \end{align*}$$

2. 2016

• Question: Evaluate $\lim_{x \to \infty} \frac{\sqrt{x^2 + 1} - \sqrt{x}}{x^2}$
• Answer: $\frac{