Answer
Please see below.
Work Step by Step
$$f(-0.1) \approx 0.25158234 \\ f(-0.01) \approx 0.25015645 \\ f(-0.001) \approx 0.25001563 \\ f(0)= \text{undefined} \\ f(0.001) \approx 0.24998438 \\ f(0.01) \approx 0.24984395 \\ f(0.1) \approx 0.24845673$$
So, we can estimate that$$\lim_{x \to 0}\frac{\sqrt{x+4}-2}{x}=0.25,$$which is confirmed by the graph of the function.
