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Suppose that f(x) is continuous in [0, 1...

Suppose that f(x) is continuous in [0, 1] and `f(0) = 0, f(1) = 0`. Prove `f(c) = 1 - 2c^(2)` for some `c in (0, 1)`

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`rArr" "f(c) = 1 - 2c^(2)`
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Suppose that f(x) is continuous in [0, 1] and f(0) = 0, f(1) = 0. Prov...

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  2. For every pair of continuous functions f,g:[0,1]->R such that max{f(x)...

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  3. Let f:R-> R and g:R-> R be respectively given by f(x) = |x| +1 and g...

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  4. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is

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  5. Q. For every integer n, let an and bn be real numbers. Let function f:...

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  6. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

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  7. "If "f(x)={{:(,-x-(pi)/(2),x le -(pi)/(2)),(,-cos x,-(pi)/(2) lt x le ...

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  8. For the fucntion f(x)=x cos ""1/x, x ge 1 which one of the following i...

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  9. Let g(x) = ((x -1)^(n))/(log cos^(m)(x-1)),0 lt x lt 2, m and n are in...

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  10. Let f and g be real valued functions defined on interval (-1, 1) such ...

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  11. In the following, [x] denotes the greatest integer less than or equal ...

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  12. If f(x)=min.(1,x^2,x^3), then

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  13. Let f(x) = ||x|-1|, then points where, f(x) is not differentiable is/a...

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  14. lff is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I, t...

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  15. The domain of the derivative of the function f(x)={t a n^(-1)x ,if|x|l...

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  16. The left hand derivative of f(x)=[x]sin(pix) at x = k, k is an intege...

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  17. Which of the following functions is differentiable at x = 0? cos (|x|...

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  18. For x in R, f(x) = | log 2- sin x| and g(x) = f(f(x)), then

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  19. If the function g(x)={{:(,k sqrt(x+1),0 le x le3),(,mx+2,3lt xle5):...

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  20. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

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  21. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

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