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Prove that the function f(x)=x^nis cont...

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

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NCERT GUJARATI-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5.1
  1. v20.1

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

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

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  4. Is the function f defined by f(x)={{:(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 byf(x)={2x+...

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  6. f(x)={{:(|x|+3, if x le -3),(-2x, if -3 lt x lt 3 ),(6x + 2, if x ge3)...

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

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  8. Find all points of discontinuity of f, where f is defined byf(x)={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 all points of discontinuity of f, where f is defined byf(x)={x^3...

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

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  12. Is the function defined by f(x)={x+5, ifxlt=1x-5, ifx >1 a continuous...

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

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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 -1lt x le 1),(2"," if x gt 1):}

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

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

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

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

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