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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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CENGAGE ENGLISH-LIMITS-Single Correct Answer Type
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  2. lim(x-(pi)/(2)) [([sinx]-[cosx]+1)/(3)]= (where [.] denotes the greate...

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  3. lim(xrarr(-1)/(3)) (1)/(x)[(-1)/(x)]= (where [.] denotes the greatest ...

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  4. Iff(x)={x+1/2, x<0 2x+3/4,x >+0 , then [(lim)(xvec0)f(x)]= (where [.] ...

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  5. lim(xrarr-7) ([x]^(2)+15[x]+56)/(sin(x+7)sin(x+8))= (where [.] denote...

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  6. Which of the following limits exists finitely?

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  7. Let L(1)=lim(xrarr4) (x-6)^(x)and L(2)=lim(xrarr4) (x-6)^(4). Which ...

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  8. Set of all values of x such that lim(nrarroo) (1)/(1+((4tan^(-1)(2pix)...

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  9. lim(xrarroo) [x-log(e)((e^(x)+e^(-x))/(2))]=

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  10. lim(xrarroo) {(e^(x)+pi^(x))^((1)/(x))}= (where {.} denotes the fracti...

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  11. If (cos x)/(sin ax) is periodic function, then lim(mrarroo)(1+cos^(2...

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  12. The value of lim(xrarr0) (sqrt(1-cosx^(2)))/(1-cos x) is

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  13. lim(xrarr(pi)/(2)) (1-sinx)tanx=

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  14. The value of lim(xrarroo) x^(2)(1-cos.(1)/(x)) is

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  15. lim(xrarroo) root3(x)(root3((x+1)^(2))-root3((x-1)^(2)))=

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  16. lim(nrarroo) (3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=

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  17. undersetlim(Xrarr2^(+)) {x}(sin(x-2))/((x-2)^(2))= (where {.} denotes ...

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  18. lim(xrarroo) (cot^(-1)(sqrt(x+1)+sqrtx))/(sec^(-1){((2x+1)/(x-1))^(x)}...

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  19. lim(xrarr0) (3 tan3x-4 tan2x-tanx)/(4x^(2)tanx)

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  20. lim(xrarr0) [(sin^(-1)x)/(tan^(-1)x)]= (where [.] denotes the greatest...

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