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`lim_(x->0)f(x)=(x^3-x)/(x^2-1)`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Discuss the continuity of f(x)={(x^4-5x^2+4)/(|(x-1)(x-2)|),x!=1,2, 6...

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  2. Given f(x)=1/(x-1) . Find the points of discontinuity of the compos...

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  3. lim(x->0)f(x)=(x^3-x)/(x^2-1)

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  4. What is the range of the function f(x)=[|x-1|]/[x-1]

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  5. f(x)={|x+1|;xlt=0x ;x >0 and g(x)={|x|+1;xlt=1-|x-2|;x >1 Draw its g...

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  6. Show that the function f(x)=(x-a)^2(x-b)^2+x takes the value (a+b)/2 f...

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  7. Suppose that f(x) is continuous in [0, 1] and f(0) = 0, f(1) = 0. Prov...

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  8. Let f be a continuous function defined onto [0,1] with range [0,1]. Sh...

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  9. Leg f be continuous on the interval [0,1] to R such that f(0)=f(1)dot ...

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  10. Let f:[0,1]vec[0,1] be a continuous function. Then prove that f(x)=x f...

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  11. Discuss the continuity of the function ([.] represents the greatest ...

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  12. Discuss the continuity of the function ([.] represents the greatest ...

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  13. Discuss the continuity of the function ([.] represents the greatest ...

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  14. Draw the graph and find the points of discontinuity f(x) = [2cos x] , ...

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  15. If the function f(x)=[((x-2)^3)/a]sin(x-2)+acos(x-2),[dot] denotes the...

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  16. Discuss the continuity of f(x)=sgn(x^3-x)

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  17. Discuss the continuity of f(x)=sgn(2cosx-1)

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  18. Discuss the continuity of f(x)=sgn(x^2-2x+3)

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  19. If f(x)=sgn(2sinx+a) is continuous for all x , then find the possible ...

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  20. Discuss the continuity of f(x)=(lim)(nvecoo)(x^(2n)-1)/(x^(2n)+1)

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