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Discuss the continuity of the followin...

Discuss the continuity of the following function `f(x)={1,\ if\ x\ i s\ r a t ion a l , 0\ if\ x\ i s\ irrational`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Discuss the continuity of f(x)=(lim)(nvecoo)(x^(2n)-1)/(x^(2n)+1)

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  2. Discuss the continuity of f(x)=("lim")(nvecoo)cos^(2n)xdot

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  3. Discuss the continuity of the following function f(x)={1,\ if\ x\ i ...

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  4. Find the value of x where f(x)={x ,\ if\ x\ r a t ion a l1-x ,\ if\ x\...

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  5. If f(x)=(x+1)/(x-1)a n dg(x)=1/(x-2),t h e n discuss the continuity ...

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  6. Find the value of x in [1,3] where the function [x^2+1]([dot] represen...

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  7. Discuss the continuity of f(x)=[tan^(-1)x]([dot] represents the greate...

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  8. Discuss the continuity of f(x)={cot^(-1)x]({dot} represents the fracti...

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  9. Discuss the continuity of f(x) in [0, 2], where f(x)=(lim)(n->oo)(s...

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  10. Discuss the continuity of f(x)={x^2,xi sr a t ion a l-x^2,xi si r r a...

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  11. If y=1/(t^2+t-2),w h e r et=1/(x-1), then find the number of points wh...

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  12. Proved that: f(x)=[x\ if\ x in Q0\ if\ x !in Q\ is continuous only ...

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  13. Proved that: f(x)=[x\ if\ x in Q-x\ if\ x !in Q\ is continuous only...

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  14. Proved that: f(x)=[x\ if\ x in Q1-x\ if\ x !in Q\ is continuous onl...

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  15. Find the left and right hand derivative of the following function a...

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  16. Find the left and right hand derivative of the following function a...

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  17. Find the left and right hand derivative of the following function a...

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  18. If f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):}...

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  19. If f(x)={a x+b ,\ xlt=-1a x^3+x+2,\ x > -1 is differentiable for all...

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  20. Find derivative of : f(x)=cos x+|cos x|a t x=pi/2

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