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If f(x) is continuous in [0,1] and f(1/...

If f(x) is continuous in `[0,1] and f(1/2)=1.` prove that `lim_(n->oo)f((sqrt(n))/(2sqrt(n+1)))=1`

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A DAS GUPTA-Continuity, Differentiability and Graph of Function-Exercise
  1. If f(x)={:{(ax^(2)-b", for " 0 le x lt1),(2", for " x=1),(x+1", for " ...

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  2. If f(x)={(((1-sin^(3)x))/(3cos^(2)x)",",x lt (pi)/(2)),(a",",x=(pi)/(2...

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  3. Let f(x)=( x^2+3x-10)/(x-2), x=!2. The value f(2) = will make the fun...

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  4. If f(x) is continuous in [0,1] and f(1/2)=1. prove that lim(n->oo)f((...

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  5. If f(x) =(sin (e^(x-2)-))/(log(x-1)) then lim(xto2)f(x) is given by

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  6. If f(x)={((sqrt(1+px)-sqrt(1-px))/(x) ",", -1 le x lt 0),((2x+1)/(x-2...

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  7. The function f(x) = (log(1+ax)-log(1-bx))/x is not difined at x = 0. ...

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  8. The function f(x)={{:(|x-3|",", x ge1),(((x^(2))/(4))-((3x)/(2))+(13)/...

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  9. The range of the function f(x)=(tan(pi[x+1]))/(x^(4)+1) (where, [.] is...

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  10. The function f(x)=1+|sin x|, is

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  11. If x+ |y|=2 y, then y as a function of x is

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  12. The graph of the function, cos x cos (x +2) -cos^2 (x+1) is

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  13. यदि f(x)=x[sqrt(x)-sqrt((x+1))] हो तो-

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  14. Let f(x)=lim(ntooo)(1-x^n)/(1+x^n). Then

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  15. If both f(x) and g(x) are non-differentiable at x=a then f(x)+g(x) may...

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  16. The function f defined by f(x) =[2x^2+3 for x leq 1 and 3x+2 for x lt...

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  17. If ("lim")(xveca)[f(x)g(x)] exists, then both ("lim")(xveca)f(x)a n d(...

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  18. underset(x rarr 0) lim ((1-cos 2x)sin 5x)/(x^(2) sin 3x)

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  19. Let f(x) be a continuous function defined on [1, 3]. If f(x) takes onl...

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  20. If f(x)={x^2 if x is rational and 0, if x is irrational} , then

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