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

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

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A N EXCEL PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Examine the following functions for continuity f(x)=(x^2-25)/(x+5)

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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 a p...

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  4. Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continu...

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  5. Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continu...

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  6. Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continu...

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  7. Find all points of discontinuity of f where f is defined by f(x)={(2x+...

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

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  9. Evalute lim(xrarr0)f(x) , where f(x)={(absx/x, x ne 0),(0,x=0):}

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

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

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  12. Is the function defined by f(x)={(x+5","ifxle1),(x-5","ifxgt1):} a con...

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  13. Find the relation between 'a' and 'b' if the function f defined by f...

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

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  15. Discuss the continuity of the following functions: f(x)=sinx+cosx

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  16. Discuss the continuity of the following functions: f(x)=sinx-cosx

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

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  18. Find the values of k so that function f is continuous at the indicated...

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  19. Find the values of k so that function f is continuous at the indicated...

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  20. Prove that the function defined by f(x)= cosx^2 is a continuous f...

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