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If the function f(x)={{:((1-cos(ax))/(x^...

If the function `f(x)={{:((1-cos(ax))/(x^2)," when "xne0),(1," when "x=0):}` be continuous at x=0, then find the value of a.

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The correct Answer is:
`a=sqrt2`
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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(a) (LONG ANSWER TYPE QUESTIONS (I))
  1. f(x)={{:((x-1)/(x+1)", "xne1),(lamda-1","x=1):} at x = 1.

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

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

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

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

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

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

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

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

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

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

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

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  13. Determine the constants 'a' and 'b' so that the function 'f' defined b...

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  14. Determine the constants 'a' and 'b' so that the function 'f' defined b...

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  15. If the function f(x)={{:(3ax+b,"for "xgt1),(" " 11,"when " x=1),(5...

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  16. Find the values of 'a' and 'b' so that the following function is conti...

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  17. Find 'a' and 'b' if the function : f(x)={{:((sinx)/(x)" , "-2lexlt0)...

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  18. Determine the values of 'a' and 'b' such that the following function i...

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  19. Let f(x)={{:((1-sin^(3)x)/(3cos^(2)x),"if "x lt(pi)/(2)),(a,"if "x=(pi...

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  20. If the following function f (x) is continuous at x=0 , find the values...

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