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Show that the function defined by g(x)=x...

Show that the function defined by `g(x)=x-[x]` is discontinuous at all integral points which [x] denotes the greatest integer function.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5.1
  1. Find the relationship between a and b so that the function f define...

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  2. For what value of lambdais the function defined by f(x)={lambda(x^2-2...

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  3. Show that the function defined by g(x)=x-[x] is discontinuous at all i...

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  4. Is the function defined by f(x)=x^2-sinx+5continuous at x=pi?

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  5. Discuss the continuity of the following functions a) f(x)=sinx+cosx

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  6. Discuss the continuity of f(x)=sinx-cosx

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  7. Discuss the continuity of the following functions : f(x)=sinx*cosx

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  8. Discuss the continuity of the cosine, cosecant, secant and cotangen...

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  9. Find all points of discontinuity of f, wheref(x)={(sinx)/x , ifx<0x+1,...

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  10. Determine if f defined by : f(x)={{:(x^(2)"sin"1/x", if "xne0),(0"...

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  11. Examine the continuity of f, where f is defined by : f(x)={{:(sinx+c...

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  12. Find the value of k so that the function f defined by f(x)={(kcosx)/(...

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  13. f(x) = {{:(kx^(2)"," if x le 2),(3", " if x gt 2):} at x = 2

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  14. Find the values of k so that the function f is continuous at the in...

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  15. Find the values of k so that the function f is continuous at the indi...

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  16. Find the value of 'a' and 'b' such that the function defined by : f(...

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  17. If f(x)=((3x+tan^(2) x)/x) is continuous at x=0, then f(0) is equal to...

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  18. Show that the function defined by f(x) = | cos x |is a continuous fun...

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  19. Examine that sin|x| is a continuous function.

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  20. Find all the points of discontinuity of f defined by f(x)" "=" "|" ...

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