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Let f(x)={{:((1-sin^(3)x)/(3cos^(2)x),"i...

Let `f(x)={{:((1-sin^(3)x)/(3cos^(2)x),"if "x lt(pi)/(2)),(a,"if "x=(pi)/(2)),((b(1-sinx))/((pi-2x)^(2)),"if "x gt(pi)/(2)):}" ,"`
if f (x) is continuous at `x=(pi)/(2)` , find a and b .

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The correct Answer is:
`p=1/2,q=4`
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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(a) (LONG ANSWER TYPE QUESTIONS (I))
  1. Find the values of a and b such that the function defined by f(x) = ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Discuss the continuity of the function of given by f(x)=+x-1|+|x-2|a t...

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  19. Find the points of discontinuity, if any, of the following function...

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  20. Discuss continuity of |x|.

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