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Show that the function f(x)=(x-a)^2(x-b)...

Show that the function `f(x)=(x-a)^2(x-b)^2+x` takes the value `(a+b)/2` for some value of `x in [a , b]dot`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. What is the range of the function f(x)=[|x-1|]/[x-1]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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