Topic: Engineering Mathematics
Evaluate $\lim_{x \to 2} \frac{\sqrt{x²+5}-3}{x²-2x}$
- A. 1/3
- B. $\infty$
- C. -3
- D. 0
Answer: A. 1/3
Explanation: This limit is of the form $0/0$. Applying L'Hospital's rule, we differentiate the numerator and denominator: $\lim_{x \to 2} \frac{\frac{d}{dx}(\sqrt{x²+5}-3)}{\frac{d}{dx}(x²-2x)} = \lim_{x \to 2} \frac{\frac{2x}{2\sqrt{x²+5}}}{2x-2}$. Substituting $x=2$ yields $\frac{2/\sqrt{9}}{2} = \frac{2/3}{2} = 1/3$.