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Prove that the function f(x)= x^(n) is c...

Prove that the function `f(x)= x^(n)` is continuous at x= n, where n is a positive integer

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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Exercise-5.1
  1. Examine the following functions for continuity. f(x)= (x^(2)-25)/(x+...

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  2. Examine the following functions for continuity. f(x) = |x-5|

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  3. Prove that the function f(x)= x^(n) is continuous at x= n, where n is ...

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  4. Is the function f defined by f(x)= {(x",","if" x le 1),(5",","if" x gt...

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  5. f(x)= {(2x+3",","if" x le 2),(2x-3",","if" x gt 2):}

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  6. f(x)= {(|x|+3",","if" x le -3),(-2x",","if"-3 lt x lt 3),(6x + 2 ",","...

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  7. f(x) = {((|x|)/(x)",","if" x ne 0),(0",","if" x= 0):}

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  8. f(x)= {((x)/(|x|)",","if" x lt 0),(-1",","if" x ge 0):}

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  9. f(x)= {(x+1",","if" x ge 1),(x^(2) + 1",","if " x lt 1):}

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  10. f(x) = {(x^(3)-3",","if" x le 2),(x^(2)+1 ",","if " x gt 2):}

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  11. f(x)= {(x^(10)-1",","if" x le 1),(x^(2)",","if" x gt 1):}

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  12. Is the function defined by f(x)= {(x+5",","if" x le 1),(x-5",","if" x ...

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  13. f(x) = {(3",","if" 0 le x le 1),(4",","if" 1 lt x lt 3),(5",","if" 3 l...

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  14. f(x)= {(2x",","if" x lt 0),(0",","if" 0 le x le 1),(4x",","if" x gt 1)...

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  15. f(x)= {(-2",","if" x le -1),(2x",","if" -1 lt x le 1),(2",","if " x gt...

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  16. Find the relationship between a and b so that the function f defined b...

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  17. For what value of lamda is the function defined by f(x)= {(lamda(x^(2)...

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

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  19. Is the function defined by f(x)= x^(2)- sin x + 5 continuous at x= pi...

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  20. Discuss the continuity of the following functions: f(x)= sin x + cos...

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