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The fuction f(x) is defined in the inter...

The fuction f(x) is defined in the interval [0,1] as follows:
`f(x)={:{(0", "x=0),(1/2-x", " 0ltxlt1/2),(1/2", " x=1/2),(2/3-x", " 1/2 lt x lt1),(1"," " "x=1):}`
Discuss the continuity of the function at `x=1/2`

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The correct Answer is:
discontinuous at `x=1/2`
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NAGEEN PRAKASHAN-Continuity and Differentiability-Exercies 5a
  1. If f(x) f(x)={((x^2-9)/(x-3)","" " xne3),(" 6""," " "x = 3")...

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  2. Discuss the continuity of the function f(x)={(x", " x ge 0),(2", "...

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  3. The fuction f(x) is defined in the interval [0,1] as follows: f(x)={...

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  4. Discuss the continuity of the function = f(x)={(3-x", "x le 0),(x...

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  5. Show that the function f(x)={(x-4", "x le 5),(5x-24", "xgt5):}...

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  6. Discuss the continutily of the following fuction at x=1 and 2 f(x)...

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  7. If f(x)={(x^2+1", "x ne 1),(" "3 ", "x=1):} , then check whethe...

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  8. Discuss the continuiy of the function f(x)={(1/x ", " x ne 0),(1...

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  9. Discuss the continuity of the function f(x)={((|x|)/x", " xne 0)...

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  10. (i) Dissusse the continuity of the function f(x)={(|x-a|", " xne a...

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  11. Show that f(x) = sinx is continuous for all values of x.

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  12. Prove that f(x) = {sinx/x ; x != 0 and 1 ; x=0. is continuous at x=0...

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  13. If f(x) ={:{((sin 3x)/(sin 5x)", "x ne 0),(0", " x= 0):}, then d...

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  14. Show that the function f(x) ={:{((sin 3x)/(x)", "x ne 0),(1", " ...

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  15. Discuss the continuity of f(x) ={:{((sin^2 2x)/(x^2)", "x ne 0),(1", ...

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  16. Discuss the continuity of f(x) ={:{(cos""(1)/(x)", "x ne 0),(" "1",...

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  17. Discuss the continuity of f(x) ={:{(sin""(1)/(x)", "x ne 0),(" "1", ...

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  18. Discuss the continutiy of f(x) ={:{(xcos""(1)/(x)", "x ne 0),(" "0...

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  19. Disuss the continutiy of f(x) ={:{((sin^2 x)/(x^2)", "x ne 0),(" "0"...

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  20. If the function f(x) ={:{((3x^3-2x^2-1)/(x-1)", "x ne 1),(" "K", ...

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