Evaluate `lim_(xrarr5) (1-sqrt(x-4))/(x-5)`

Options

A. `-1/2`
B. `-1`
C. `-2`
D. `0`

Answer

A

Explanation

`underset(xrarr5)"lim"(1-sqrt(x-4))/(x-5)`
`=underset(xrarr5)"lim"(1-sqrt(x-4))/(x-5)xx(1+sqrt(X-4))/(1+sqrt(x-4))`
`=underset(xrarr5)"lim"(1-(x-4))/((x-5)(1+sqrt(x-4))`
`=underset(xrarr5)"lim"((5x-x))/(-(5-x)(1+sqrt(x-4)))`
`=underset(xrarr5)"lim"(-1)/(1+sqrt(x-4))`
`=(-1)/(1+sqrt(5-4))=(-1)/(2)`.