Evaluate the following limit: `underset( x rarr 2) ( "lim")(sqrt(x^2+1)-sqrt(5))/(x-2)`

Options

A. `3/9`
B. `2sqrt3`
C. `4/(sqrt6)`
D. `2/(sqrt5)`

Answer

`2/(sqrt5)`

Explanation

For finding the limit of the given equation when `x` tends to `2`

Substituting `x` as `2` , we get an indeterminant form

Rationalizing the given equation


`Rightarrow lim _(x rightarrow 2) frac(sqrt(x^(2)+1)-sqrt(5))(x-2)= Rightarrow lim _(x rightarrow 2) frac((sqrt(x^(2)+1)-sqrt(5)))(x-2) frac((sqrt(x^(2)+1)+sqrt(5)))((sqrt(x^(2)+1)+sqrt(5)))`


We have the formula: `(a+b)(a-b)=a^(2)-b^(2)`


...