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Given that , f(x)={{:((1-cos4x)/(x^(2)),...

Given that , `f(x)={{:((1-cos4x)/(x^(2)),"if "xlt0),(" a ","if "x=0),((sqrt(x))/(sqrt(16+sqrt(x))-4),"if "xgt0):}`
If f (x) is continuous at x= 0 , find the value of a

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The correct Answer is:
a = 8
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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(a) (LONG ANSWER TYPE QUESTIONS (I))
  1. For what value of 'k' is the function defined by : f(x)={{:(k(x^(2)+...

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

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

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

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

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

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

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

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

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

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

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

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  13. If f(x) {:(=x^(2)+ax+b", if "0 le x lt 2 ),(= 3x+2", i...

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  14. Find all the points of discontinuity of the function 'f' defined by : ...

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

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  16. Find all points of discontinuity of f, where f is defined byf(x)={2x+...

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  17. Show that the function defined by f(x)" "=" "s in" "(x^2) is a cont...

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  18. Show that the function defined by f(x)=cos(x^2)is a continuous functi...

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  19. Show that the function defined by f(x) = | cos x |is a continuous fun...

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  20. Show that the function 'f' given by : f(x)=|x|+|x-1|,x inR is cont...

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