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Prove that the greatest integer function...

Prove that the greatest integer function [x] is continuous at all points except at integral points.

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The greatest integer function [x] is continous everywhere?..

The function f(x)=x-[x] , where [⋅] denotes the greatest integer function is (a) continuous everywhere (b) continuous at integer points only (c) continuous at non-integer points only (d) differentiable everywhere

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Prove that the greatest integer function [x] is continuous at all poin...

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  2. If f(x)= {(kx^2,,x,<,2),(3,,x,ge,2):} is continuous at x = 2, then the...

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  3. Check the continuity of the function f given by f(x) = 2x+3 at x=1

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  4. Check the continuity of the following functions: f(x) = x^2atx=0

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  5. Examine the continuity of the function f(x) = 2x^2 - 1 at x=3

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  6. Examine the function f(x) = 2x^2-5 for its continuity at the point x =...

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  7. Is the function defined by f(x) = |x|, a continuous function?

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  8. Find the point at which the function f(x) = [x] is not continuous in (...

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  9. Examine the following function for continuity: f(x) = x-5

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  10. Examine the following functions for continuity: f(x) = x^3 + x^2-1

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  11. Examine the following function for continuity: f(x) = 1/(x-5), x ne 5

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  12. Examine the following function for continuity: f(x) = (x^2 -25)/(x+5),...

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  13. Examine the following function for continuity: f(x) = |x-5|

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  14. Prove that the following functions are continuous at all points of the...

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  15. Prove that the following functions are continuous at all points of the...

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  16. Prove that the following functions are continuous at all points of the...

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  17. Discuss the continuity of the following function: f(x) = sinx + cosx

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  18. Discuss the continuity of the following function: f(x) = sinx cdot cos...

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  19. Discuss the continuity of the following function: f(x) = sinx cdot cos...

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  20. Discuss the continuity of the following functions: f(x) = (sinx)/(co...

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  21. Prove that f(x) = |sin x| is continous at all point of its domnin.

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