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

Show that the function defined by `g(x) = x-[x]` is discontinuous at all integral points. Here `[x]` denotes the greatest integer less than or equal to x.

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Find f(0) if the function defined as f(x) = {:{(log(1+x/a)-log(1-x/b))...

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  2. For what value of lambda is the function defined by f(x) = {:{lambda(x...

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

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  4. Show that the function f(x) = |sin x + cos x | is continuous at x = pi...

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  5. Extend the defination of the functionf(x) = (1-cos[7(x-pi)])/(5(x-pi)^...

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  6. Let f(x) = {:{(4x-3, if x<0),(4x + 3, if x ge 0):}. Is it a continuous...

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

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  8. Prove that the following functions are continuous: cot x

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  9. Prove that the following functions are continuous: sec x

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  10. Prove that the following functions are continuous: sin^-1x

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  11. Prove that the function f defined by f(x) = x^3 + x^2 -1 is a continuo...

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  12. Prove that the following functions are continuous: |x+1| +| x|

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  13. Prove that the following functions are continuous: sin |x|

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  14. Prove that the following functions are continuous: |sin x|

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  15. Prove that the following functions are continuous: |cos x|

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  16. Prove that the following functions are continuous: cosx^2

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  17. Show that the following functions are continuous: f(x) = sin(x^2)

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  18. Prove that the following functions are continuous: e^(cosx)

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  19. Prove that the following functions are continuous: e^x(tanx)

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  20. Prove that the following functions are continuous: (x^2 + x+1)/((x-1...

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