Evaluate the following limit : lim(x →1) √(x + 8)/√x

Question

Evaluate the following limit : \(\lim\limits_{\text x \to 1}\cfrac{\sqrt{\text x+8}}{\sqrt {\text x}} \)

lim(x →1) √(x + 8)/√x

Answer 1

Given limit 

\(\Rightarrow\lim\limits_{\text x \to 1}\cfrac{\sqrt{\text x+8}}{\sqrt {\text x}} \)

Putting the values of limits directly, i.e. x = 1, we have

Hence the value of the given limit is 3.