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If f(x)=|x-1|-[x], where [x] is the grea...

If `f(x)=|x-1|-[x]`, where `[x]` is the greatest integer less than or equal to x, then

A

`underset(xto0)lim[f(x)]=0`

B

`underset(xto0)lim[f(x)]=1`

C

`underset(xto0)lim[(f(x))/(x)]` does not exist

D

`underset(xto0)lim[(f(x))/(x)]` exists

Text Solution

Verified by Experts

The correct Answer is:
A, D
`f(1+0)=underset(hto0)lim(|1+h-1|-[1+h])=underset(hto0)lim(h-1)=-1`
`f(1-0)=underset(hto0)lim(|1-h-1|-[1-h])=underset(hto0)lim(h-0)=0`
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CENGAGE-LIMITS-Exercise (Multiple)
  1. Let f(x)={{:(1+(2x)/(a)", "0lexlt1),(ax", "1lexlt2):}."If" lim(xto1)...

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  2. If f(x)=|x-1|-[x], where [x] is the greatest integer less than or equa...

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  3. If lim(ntooo) (an-(1+n^(2))/(1+n))=b, where a is a finite number, then

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  4. If m,n inN,lim(xto0) (sinx^(n))/((sinx)^(m)) is

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  5. Let f(x)={{:(x^(n)sin(1//x^(2))","xne0),(0", "x=0):},...

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  6. If L=lim(xto0) (1)/(x^(3))((1)/(sqrt(1+x))-(1+ax)/(1+bx)) exists,then

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  7. Which of the following is true ({.} denotes the fractional part of the...

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  8. Which of the following is/are correct?

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  9. If lim(xto1) (2-x+a[x-1]+b[1+x]) exists, then a and b can take the val...

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  10. Let L=lim(xtoa) (|2sinx-1|)/(2sinx-1). Then

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  11. Let f(x)=lim(ntooo) (x)/(x^(2n)+1). Then

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  12. lim(ntooo) (-3n+(-1)^(n))/(4n-(-1)^(n)) is equal to (n inN)

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  13. Given a real valued function f such that f(x)={tan^2[x]/(x^2-[x]^2) ,...

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  14. If f(x)=(3x^2+a x+a+1)/(x^2+x-2), then which of the following can be c...

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  15. The value of lim(ntooo) (1)/(1+nsin^(2)nx)" can be " (n inN)

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  16. Let f(x) = (x^2-9x+20)/(x-[x]) where [x] denotes greatest integer less...

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  17. Given lim(x to 0)(f(x))/(x^(2))=2, where [.] denotes the greatest inte...

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  18. If f(a)=lim(xto2)(sin^(x)a+cos^(x)a)^((1)/((x-2)))" for "ain[0,(pi)/(2...

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