Question

Complete the table and estimate the limit

Answer 1

`\lim_(x \to 0) (√(x+5)-√(5) )/(x) =(√(5))/(10)`

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,
`\lim_(x \to 0) (√(x+5)-√(5) )/(x) =(√(5))/(10)`