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Find the value of ' a^(prime) for which ...

Find the value of `' a^(prime)` for which the function `f` defined by `f(x)={asinpi/2(x+1),\ \ \ xlt=0(tanx-sinx)/(x^3),\ \ \ x >0` is continuous at `x=0` .

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The correct Answer is:
`a= (1)/(2)`
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OSWAAL PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-CONTINUITY ( 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. Find the value of the constant k so that the function f , defined belo...

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  3. Let : f(x) {:(=(1-cos 4x)/(x^(2))", ... "x lt 0 ),(= a", ...

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  4. If f(x)={{:(1" if "x le 3),(ax+b" if "3 lt x lt 5),(7" if "x ge 5):} ...

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  5. f(x) = {{:((sqrt(1+kx)-sqrt(1-kx))/(x),if -1 le x lt 0),((2x+1)/(x-1...

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  6. f(x)={(x^3+x^2-16 x+20)/((x-2)^2), x!=2k ,k , x=2 . Find the value of ...

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  7. Find the values of k so that the function f is continuous at the in...

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

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  9. Discuss the continuity of the function f(x) at x= (1)/(2), when f(x) i...

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  10. Find the value of ' a ' if the function f(x) defined by f(x)={2x-1,\ \...

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  11. Find the value of ' a^(prime) for which the function f defined by f(x)...

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  12. Find all the points for discontinuity of the function f(x) =[x^2] on [...

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  13. f(x)={{:(|x|+3, if x le -3),(-2x, if -3 lt x lt 3 ),(6x + 2, if x ge3)...

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  14. For what value of k is the function defined by f(x)={{:(k(x^(2)+2)," i...

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  15. Find the values of a and b such that the function defined as follows i...

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  16. Find the values of k so that the function f is continuous at the in...

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  17. If the functions f(x) , defined below is continuous at x=0 , find t...

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  18. Show that the function f(x)=|x-2| is continuous but not differentiable...

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  19. Show that the function f defined as follows, is continuoius at x=2, bu...

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  20. Show that the function f(x)=|x-3|,\ x in \ |R , is continuous but n...

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