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COnsider g(x)=(8)/(x-6) on (6,13)

(a) Is this function continuous on the given interval? If it is continuous, type "continuous". If not, give the x -value where the function is not continuous.
Is is continous? If not? what interval then?

  • Calculus -

    It depends on whether the round brackets surrounding your interval of (6,13) indicate that the numbers 6 and 13 are not included in the interval. The notation I'm familiar with uses square brackets to indicate that the numbers ARE included, and round brackets to indicate that they're NOT. On that basis, the interval (6,13) would NOT include the value 6, in which case the function is continuous over the given range. Had the interval read [6,13], to me this would mean that the interval DOES include 6, and that therefore the function is discontinuous at x=6 (since g(6)=8/0, which is undefined). Whether your brackets mean the same to you as they would to be I have no idea: you would need to check your definitions.

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