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Evaluate lim(xrarr5) (1-sqrt(x-4))/(x-5)...

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

A

`-1/2`

B

`-1`

C

`-2`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
A

`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)`.
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NAGEEN PRAKASHAN-LIMITS AND DERIVATIVES-Miscellaneous Exercise
  1. Evaluate lim(xrarr5) (1-sqrt(x-4))/(x-5)

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