Calculating Limit of Function – A quotient of functions with square roots – Exercise 6217

Exercise

Evaluate the following limit:

$$\lim _ { x \rightarrow \infty} \frac{\sqrt{x^3+x^2}-\sqrt{x^3-1}}{\sqrt{x}}$$

$$\lim _ { x \rightarrow \infty} \frac{\sqrt{x^3+x^2}-\sqrt{x^3-1}}{\sqrt{x}}=\frac{1}{2}$$