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Iff(x)={x+1/2, x<0 2x+3/4,x >+0 , then [...

If`f(x)={x+1/2, x<0 2x+3/4,x >+0` , then `[(lim)_(xvec0)f(x)]=` (where [.] denotes the greatest integer function) a. b. c. does not exist d. none of these

A

`(1)/(2)`

B

`(3)/(4)`

C

does not exist

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(xrarr0^(-))(lim)f(x)=underset(xrarr0^(-))(lim)(x+(1)/(2))=(1)/(2)`
`underset(xrarr0^(+))(lim)f(x)=underset(xrarr0^(+))(lim)(2x+(3)/(4))=(3)/(4)`
`therefore" "underset(xrarr0)(lim)f(x)` does not exist.
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