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Consider the function f defines by f(x) ...

Consider the function f defines by` f(x) = x-[x]`, where[x] denotes the greatest integral function. Show that the function is discontinous for integral values of x and continous for all other values.`

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A DAS GUPTA-Continuity, Differentiability and Graph of Function-Exercise
  1. Discuss the continuity of f(x)=(lim)(nvecoo)(x^(2n)-1)/(x^(2n)+1)

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  2. The function f(x). defined as f(x)=lim(n->oo)(f(x)+x^(2n)g(x))/(1+x^(2...

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  3. Consider the function f defines by f(x) = x-[x], where[x] denotes the ...

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  4. The values of a and b so that the function f(x) = {{:(x + a sqrt(2) si...

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  5. Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is contin...

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  6. Leg f(x+y)=f(x)+f(y)fora l lx , y in R , If f(x)i scon t inuou sa tx=...

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  7. Let f (x+y)=f (x) f(y) AA x, y in R , f (0)ne 0 If f (x) is continous ...

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  8. Let f : [0, 1] rarr [0, 1] be a continuous function such that f (f (x)...

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  9. The set of all points, where the function f (x) = x/(1+|x|) is dif...

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  10. The set of points where ,f(x) = x|x| is twice differentiable is

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  11. Let f(x) be difined in the interval [-2, 2] such that f(x)={{:(-1"...

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  12. Let f(x) = {{:(x^(2)/2", "0 lexlt1),(2x^(2)-3x+3...

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  13. Draw the graph of the function and discuss the continuity and differen...

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  14. Given the function f(x) = 1/( 1-x) , The points of discontinuity of th...

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  15. If f(x)={:{(ax^(2)-b", for " 0 le x lt1),(2", for " x=1),(x+1", for " ...

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

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

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

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

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

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