Evaluate the following limit: `underset( x rarr 1) ( "lim")(x-1)/(sqrt(x^2+3)-2)`

Options

A. `1sqrt4`
B. `2sqrt(6)`
C. `2sqrt(5)`
D. `frac(2)(sqrt(5))`

Answer

`frac(2)(sqrt(5))`

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)`


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