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Let f : R to [0,oo)" be such that "under...

Let `f : R to [0,oo)" be such that "underset(x to 5)lim f(x)" exists and "underset(x to 5)lim ([f(x)]^(2)-9)/(sqrt(|x-5|))=0." Then "underset(x to 5)lim f(x)` is equal to:

A

1

B

2

C

3

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
`lim_(xto5)((f(x))^2-9)/(sqrt(|x-5|))=0`
` rArr lim_(xto5)(f(x))^2-9=0`
` rArr l^2-9=0, "where" lim_(xto5)f(x)=l`
`rArr l= +-3`
`rArr l=3 [because f(x)ge 0 " for all " x in R ]`
`rArr lim_(xto5)f(x)=3`
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