Evaluate the following limit: `underset( x rarr 7) ( "lim")(4-sqrt(9+x))/(1-sqrt(8-x))`

Options

A. `-3/7`
B. `sqrt6`
C. `-frac(1)(4)`
D. all of the above

Answer

`-frac(1)(4)`

Explanation

For finding, the limit of the given equation when `x` tends to `7`

Substituting `x` as `7` , we get an indeterminant form

Rationalizing the given equation


=`Rightarrow lim _(x rightarrow 7) frac((4-sqrt(9+x)))((1-sqrt(8-x))) frac((1+sqrt(8-x)))((1+sqrt(8-x))) frac((4+sqrt(9+x)))((4+sqrt(9+x)))`


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


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