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Test for continuity of the following fun...

Test for continuity of the following function at `x = a`: f(x)={(x-, a) `sin(1/(x-a)`, where `x!=a` (x- a) 0 ,when `x = a`

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The correct Answer is:
Continuous
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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(a) (LONG ANSWER TYPE QUESTIONS (I))
  1. Test for continuity of the following function at x = a: f(x)={(x-, a) ...

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  2. Examine the function for continuity at x = 0 : f(x)={{:(sinx/x" wh...

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  3. Discuss the continuity of f(x) at x = 0 if : f(x)={{:((sqrt(1+x)-sqr...

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  4. f(x) = {{:(kx^(2)"," if x le 2),(3", " if x gt 2):} at x = 2

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  5. The function is defined by f(x) = {(kx+1,if, x lepi),(cos x,if, x gt p...

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  6. If the function f(x) = {(kx + 5 ", when " x le 2),(x -1 ", when " x gt...

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  7. f(x)={{:(3k-2x", when "xlt1),(2k+1", when "xge1):} at x = 1

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  8. f(x)={{:(3x-8, if x le 5),(2k, if x gt 5) :} at x = 5

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  9. f(x)={{:((x-1)/(x+1)", "xne1),(lamda-1","x=1):} at x = 1.

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  10. f(x) = {{:((1-cosAx)/(x sinx), if x ne 0),(1/2, if x = 0):} at x = 0

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  11. If the function f(x)={{:((1-cos(ax))/(x^2)," when "xne0),(1," when "x=...

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  12. f(x)={{:((sin2x)/(5x)",when "xne0),(m", when "x=0):} at x = 0

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  13. Let f(x)={:{((kcosx)/(pi-2x)',xne(pi)/(2)),(3",",x=(pi)/(2).):} If l...

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  14. f(x) = {{:((k cosx )/((pi - 2x)"," if x ne (pi)/(2))),(3"," if x = (p...

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  15. f(x)={{:((x^(2)-9)/(x-3)",when "xne3),(k", when "x=3):} at x = 3

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  16. f(x)={{:(((x+3)^(2)-36)/(x-3)", "xne3),(k" , "x=3):} at ...

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  17. For what value of 'k' is the function defined by : f(x)={{:(k(x^(2)+...

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  18. If the function defined by : f(x)={{:(2x-1", "xlt2),(a", "x...

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  19. Given that , f(x)={{:((1-cos4x)/(x^(2)),"if "xlt0),(" a ","if "x=0)...

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  20. Find the values of a and b such that the function defined by f(x) = ...

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