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Let f(x)={{:(" "x^(2)/(2),"when " 0...

Let `f(x)={{:(" "x^(2)/(2),"when " 0lexlt1),(2x^(2)-3x+(3)/(2),"when " 1 lexle2):}`
Discuss the continuity of (x) in the interval `0lexle2` .

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The correct Answer is:
Continuous on the right of the point x = 0 , continuous for all x in `0ltxlt2` and continuous on the left x = 2
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CHHAYA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -EXERCISE 2A ( Long Answer Type Questions)
  1. Given , f(x)={{:((sin5x)/(3x),"when "xne0),((3)/(5),"when "x=0):} Ex...

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  2. Let f(x)={{:(" "x^(2)/(2),"when " 0lexlt1),(2x^(2)-3x+(3)/(2),"wh...

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  3. Show that function f(x) = 2x-|x| is continous at x=0.

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  4. Test the continuity of the function f (x) : f(x)={{:(x^(2)sin.(1)/(...

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  5. A function f (x) is defined as follows : f(x)={{:(3x+1,"for "xle1 ),(...

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  6. A function f (x) is defined as f(x)={{:(ax+2,"when "xle3),(bx+3,"whe...

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

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

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

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

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

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

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

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

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

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

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

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

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