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Is the function f defined by {{:(x," i...

Is the function f defined by
`{{:(x," if "x le 1),(5," if "x gt 1):}`
continuous at x= 0? At x=1? At x=2?.

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Verified by Experts

The correct Answer is:
f is continuous at x=0 and x=2; not continuous at x=1.
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NCERT BANGLISH-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5.1
  1. Examin the following functions for continuity. f(x)= |x-5|.

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  2. Prove that the function f(x)= x^(n) is continuous at x= n, where n is ...

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  3. Is the function f defined by {{:(x," if "x le 1),(5," if "x gt 1):} ...

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  4. Find all points of discontinuity of f, where f is defined by f(x) =...

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  5. Find all the points of discontinuity of f defined by f(x)= |x|-|x+1|.

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  6. Find all points of discontinuity of f, where f is defined by f(x) =...

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  7. Find all points of discontinuity of f, where f is defined by f(x)={...

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  8. Find all points of discontinuity of f, where f is defined by f(x)={...

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  9. Find all points of discontinuity of f, where f is defined by f(x)={...

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  10. Find all points of discontinuity of f, where f is defined by f(x)={...

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  11. Is the function defined by f(x)={{:(x+5," if "x le1),(x-5," if "x gt...

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  12. Discuss the continuity of the function f, where f is defined by f(x)...

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  13. Discuss the continuity of the function f, where f is defined by f(x)...

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  14. Discuss the continuity of the function f, where f is defined by f(x)...

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  15. Find the relationship between a and b so that the function f defined b...

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  16. For what value of lambda is the function defined by f(x)={{:(lambda(...

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  17. Show that the function defined by g(x) = x-[x] is a discontinuous at a...

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  18. Is the function defined by f(x)= x^(2)-sin x+5 continuous at x= pi?

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  19. Discuss the continuity of the following functions : f(x)= sin x +cos...

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  20. Discuss the continuity of the following functions : f(x)= sin x - co...

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