Evaluate the following limit: `underset( x rarr 2) ( "lim")(sqrt(1+4x)-sqrt(5+2x))/(x-2)`

Options

A. `5`
B. `6/8`
C. `sqrt3`
D. `1/3`

Answer

`1/3`

Explanation

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

Substituting `x` as `2` , we get an indeterminant form of `0/0`

Rationalizing the given equation


Evaluate,
`Rightarrow lim _{x rightarrow 2} frac{sqrt{1+4 x}-sqrt{5+2 x}}{(x-2)}` as `x rightarrow 2`

it is `frac{0}{0}`
From so,
...