Calculating Limit of Function – A quotient of functions with a square root – Exercise 5925

Exercise

Evaluate the following limit:

$$\lim _ { x \rightarrow 0} \frac{\sqrt{1+x+x^2}-1}{x}$$

$$\lim _ { x \rightarrow 0} \frac{\sqrt{1+x+x^2}-1}{x}=\frac{1}{2}$$