Answer:
[tex]\lim_{x \to 0} \frac{\sqrt{x+5}-\sqrt{5} }{x} =\frac{\sqrt{5}}{10}[/tex]
Step-by-step explanation:
If x=-0.1, then f(x)=0.2247361538
If x=-0.01, then f(x)=0.2237187131
If x=-0.001, then f(x)=0.2236179792
If x=0.001, then f(x)=0.2235956185
If x=0.01, then f(x)=0.223495106
If x=0.1, then f(x)=0.2224998063
We can see that as x approaches 0, we see that f(x) gets closer to √5/10
Therefore, [tex]\lim_{x \to 0} \frac{\sqrt{x+5}-\sqrt{5} }{x} =\frac{\sqrt{5}}{10}[/tex]
