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A function is defined as, f(x)={(0, whe...

A function is defined as,
`f(x)={(0, where x is rational),(1, where x is irrational)}:`. Then f(x) is

A

continuous for all `x in R`

B

continuous for all `x in R-{0}`

C

continuous for all `x in R-{0,1}`

D

discontinuous for all `x in R`

Text Solution

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The correct Answer is:
D
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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. The value of lim(xrarr0)(1^x+2^x+3^x+...+n^x)^(a//x)/n, is:

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  2. If lim(xrarr0)(1+ax+bx^2)^(2//x)=e^3, then the value of a and b, is :

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  3. A function is defined as, f(x)={(0, where x is rational),(1, where x ...

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  4. If f(x)={(-1, xlt0 ),(0, x =0),(1, x gt 0):} and g(x)=x(1-x^2), then...

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  5. If f(x)=-1+|x-2|, 0lexle4 g(x)=2-|x|, -1lexle3 Then, fog(x) is contin...

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  6. Let f(x)=[sinx + cosx], 0ltxlt2pi, (where [.] denotes the greatest int...

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  7. If f(x)={(sin{cosx}/(x-pi/2), x ne pi/2),(1, x=pi/2):} , where {.} den...

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  8. If f(x)=(x^3+x^2-16x+20)/(x-2)^2, x ne 2 =k, x=2 and if f(x) is con...

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  9. In the function f(x)=[(x-2)^3/a]sin(x-2)+acos(x-2), (where [.] denote...

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  10. Let f(x) = |x|+|sin x|, x in (-pi/2, (3pi)/2). Then, f is :

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  11. If f is a periodic function, then

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  12. If f(x)=[sin^2x] (where [.] denotes the greatest integer function ) th...

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  13. Let f(x) be a polynomial of degree one and f(x) be a function defined ...

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  14. lim(xrarr0)(e^cotx-e^cosx)/(cotx-cosx) is

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  15. value of lim(xrarrinfty)((x+1)/(x+2))^(2x+1) is

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  16. lim(xrarrinfty)(3^x+4^(x+1)+5^x)/(5^x+3^(x+1)) is

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  17. lim(xrarrinfty)[((2+x)^40(4+x)^5)/(2-x)^45] equals

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  18. lim(xrarr5)(x-5)/|x-5| equals to

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  19. lim(x rarr pi/3)frac(Sin(pi/3-x))(2cosx-1) is equal to

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  20. If f(x)=((x^2+5x+3)/(x^2+x+2))^x then lim(xrarrinfty)f(x)=

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