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Show that the function {{:((x^(3)-1)/(x-...

Show that the function `{{:((x^(3)-1)/(x-1)", ""if "xne1),(3", ""if "x=1):}` is continuous on `(-oo,oo)`

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For what value of alpha is this function f(x)={{:((x^(4)-1)/(x-1)", ""if "xne1),(alpha", ""if "x=1):} continuous at x = 1?

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SURA PUBLICATION-DIFFERENTIAL CALCULUS - LIMITS AND CONTINUITY-EXERCISE 9.5
  1. Examine the continuity of the following : (|x-2|)/(|x+1|)

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  2. Examine the continuity of the following : cotx+tanx

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  3. Find the points of discontinuity of the function f, where f(x)={{:(4...

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

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

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

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  7. At the given point x(0) discover whether the given function is continu...

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  8. At the given point x(0) discover whether the given function is continu...

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  9. Show that the function {{:((x^(3)-1)/(x-1)", ""if "xne1),(3", ...

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  10. For what value of alpha is this function f(x)={{:((x^(4)-1)/(x-1)", ...

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  11. Let f(x)={{:(0", ""if "xlt0),(x^(2)", ""if "0lexlt2),(4", ""if ...

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  12. If f and g are continuous functions with f(3) = 5 and lim(xto3)[2f(x)-...

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  13. Find the points at which f is discontinuous. At which of these points ...

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  14. Find the points at which f is discontinuous. At which of these points ...

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  15. Which of the following functions f has a removable discontinuity at x=...

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  16. Which of the following functions f has a removable discontinuity at x=...

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  17. Which of the following functions f has a removable discontinuity at x=...

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  18. Find the constant b that makes g continuous on (-oo,oo)" "g(x)={{:(x^(...

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  19. Consider the function f(x)=x"sin"pi/x. What value must we give f(0) in...

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  20. The function f(x)=(x^(2)-1)/(x^(3)-1) is not defined at x = 1. What va...

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