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Let f(x)={{:((1-cos2ax)/(xsin2x),"when "...

Let `f(x)={{:((1-cos2ax)/(xsin2x),"when " xne0),(" " (1)/(2),"when " x =0):}` If f (x) is continuous at x = 0 , find the value of `alpha` .

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The correct Answer is:
`a=+-1`
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CHHAYA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -EXERCISE 2A ( Long Answer Type Questions)
  1. A function f (x) is defined as f(x)={{:(ax+2,"when "xle3),(bx+3,"whe...

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  2. Let f(x)={{:((x^(3)+x^(2)-16x+20)/((x-2)^(2)),"when " xne2),(" "k,...

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  3. Let f(x)={{:((1-cos2ax)/(xsin2x),"when " xne0),(" " (1)/(2),"when " ...

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  4. If the following function f (x) is continuous at x = 0 , find k : ...

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  5. The function f(x)=(x^(3)-1)/(x-1) is undefined at x = 1 . Redefine the...

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  6. Show that the function f(x)={{:(x+(x+2)/(|x+2|),"when " xne-2),(" "-...

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

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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. Let f(x)={{:((sin(a+1)x+sinx)/(x)",","when " xlt0),(" c,","wh...

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  10. Show that the function f(x)=|sinx+cosx| is continuous at x = pi.

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  11. Show that the function g(x)=x-[x] is discontinuous at all integral po...

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  12. Find from the first principle , the derivatives of the following funct...

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  13. Find from the first principle , the derivatives of the following funct...

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  14. Find from the first principle , the derivatives of the following funct...

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  15. Find from the first principle , the derivatives of the following funct...

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  16. Find from the first principle , the derivatives of the following funct...

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  17. Find from the first principle , the derivatives of the following funct...

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  18. Find from the first principle , the derivatives of the following funct...

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  19. f(x)={{:(x^(2)-2x+3,"for "xlt1),(" "2,"for "x=1),(2x^(2)-5x+5,"for ...

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  20. A function f (x) is defined as follows : f(x)={{:(2-x",","when "xlt...

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