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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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NCERT TAMIL-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5.1
  1. Examin the following functions for continuity. f(x)= (x^(2)-25)/(x+5...

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  2. Examin 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 {{:(x," if "x le 1),(5," if "x gt 1):} ...

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  5. Find all points of discontinuity of f, where f is defined by f(x) =...

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  6. Find all points of discontinuity of f, where f is defined by f(x)={...

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  7. Find all points of discontinuity of f, where f is defined by f(x) =...

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  8. Find all points of discontinuity of f, where f is defined by f(x)={...

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  9. Find all points of discontinuity of f, where f is defined by f(x)={...

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  10. Find the points of discontinuity of the function f, where f(x)={{:(x...

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  11. Find all points of discontinuity of f, where f is defined by f(x)={...

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  12. Is the function defined by f(x)={{:(x+5," if "x le1),(x-5," if "x gt...

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  13. Discuss the continuity of the function f, where f is defined by f(x)...

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  14. Discuss the continuity of the function f, where f is defined by f(x)...

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  15. Discuss the continuity of the function f, where f is defined by f(x)...

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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 lambda is the function defined by f(x)={{:(lambda(...

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  18. Show that the function defined by f(x)= cos (x^2) is a continuous func...

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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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