Question

The value of $\underset{x\to \infty }{\lim }\frac{\sqrt{1+x^4}+\left(1+x^2\right)}{x^2}$ is

(a) −1
(b) 1
(c) 2
(d) none of these

Answer 1

(c) 2

$$\begin{gathered} \underset{x\to \infty }{\lim }\frac{\sqrt{1+x^4}+\left(1+x^2\right)}{x^2} \\ =\underset{x\to \infty }{\lim }\sqrt{\frac{1}{x^4}+1}+\frac{1}{x^2}+1 \\ =2 \end{gathered}$$