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Continuous function

  • Thread starter kieranl
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  • #1
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Homework Statement



Determine whether the function is continuous, piecewise continuous or neither on the segment [0, 10] and sketch the graph of f(t).

f(t)= {10-t, 0<=t<=8 and 10, 8<=t<=10)

The Attempt at a Solution



I would say that it was neither as the right hand limit at t = 8 doesnt equal the left hand limit. But im not sure wat the difference is between a continuous function and a piecewise continuous function???

thanks for any help
 

Answers and Replies

  • #2
Dick
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You are absolutely right. A piecewise continuous function is continuous on the interior of each of the pieces, a continuous function is continuous everywhere.
 
  • #3
HallsofIvy
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No, Dick, NOT "absolutely right". That function is equal to 10- t for [itex]0\le t\le 8[/itex] and 10 for [itex]8\le t\le 10[/itex] so it is continuous on the interior of each of those intervals and is "piecewise continuous", not "neither".
 
  • #4
Dick
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No, Dick, NOT "absolutely right". That function is equal to 10- t for [itex]0\le t\le 8[/itex] and 10 for [itex]8\le t\le 10[/itex] so it is continuous on the interior of each of those intervals and is "piecewise continuous", not "neither".


Right. I only saw that 'the limit doesn't exist' and missed the 'neither'. Thanks.
 

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