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Discuss the continuity of f(x)={cot^(-1)...

Discuss the continuity of `f(x)={cot^(-1)x]({dot}` represents the fractional part function).

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Find the value of x in [1,3] where the function [x^2+1]([dot] represen...

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

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

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

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  5. 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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  6. 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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  7. Proved that: f(x)=[x\ if\ x in Q0\ if\ x !in Q\ is continuous only ...

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

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

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

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

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

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

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

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

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  16. The number of points at which the function, f (x)={{:(min {|x|"," x ...

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  17. If incident ray from point (-3, 2) parallel to the axis of parabola...

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  18. Let f be differentiable at x=a\ a n d\ l e t\ f(a)!=0. Evaluate (lim)(...

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  19. Show that the function f(x)={x^msin(1/x)0 ,x!=0,x=0 is differentiab...

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  20. Let f(x)=sgn(x) and g(x)= x(1-x^2), The number of points at which f(...

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