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Prove that every rational function is co...

Prove that every rational function is continuous.

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V PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Show that every polynomial function is continuous

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  2. Prove that the greatest integer function f : R rarrR given by f(x) =[x...

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  3. Prove that every rational function is continuous.

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  4. Discuss the continuity of sine function.

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  5. Show that the function defined by f(x)=sin (x^2) is a continuous funct...

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  6. Prove that the function f(x)=5x-3 is continuous at x=0, at x=-3 and at...

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  7. Examine the continuity of the function f(x)=2x^2-1 at x=3

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  8. Examine the following functions for continuity f(x)=1/(x-5)

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

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

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

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

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

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

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  15. Examine the continuity of the function <be> f(x)={(x+1,xge1),(x^2+1,x<...

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  16. Examine the continuity of the function f(x)={(x^3-3, if ,x le 2),...

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  17. Examine whether the function defined by f(x)={(x+5,xle1),(x-5,x>1):}...

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  18. Discuss the continuity of the function f(x)={(2 x , if , xlt0),( 0,...

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  19. Find the derivative of the function given by f(x)=sin (x^2)

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  20. Differentiate the function f(x)=sin [cos x^2] with respect to x.

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