If f: RvecR is defined by f(x)=[x-3]+|x-...

If `f: RvecR` is defined by `f(x)=[x-3]+|x-4|` for `x in R ,` then `(lim)_(xvec3)f(x)` is equal to (where [.] represents the greatest integer function) a. b. c. d. -1

A

`-2`

B

`-1`

C

0

D

1

Text Solution

Verified by Experts

The correct Answer is:

C

Given that,
`f(x)=[x-3]+[x-4]`
`therefore" "underset(xrarr3^(+))limf(x)=underset(xrarr3^(-))lim([x-3]+[x-4])`
`=underset(hrarr0)lim([3-h-3]+|3-h-4|)`
`=underset(hrarr0)lim([-h]+1h)`
`=-1+1+0=0`

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