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Carla1985
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I need to find a function that is continuous at 0 but discontinuous at every other point. IV been stuck on this for hours now :( thankyou
Carla1985 said:I need to find a function that is continuous at 0 but discontinuous at every other point. IV been stuck on this for hours now :( thankyou
Carla1985 said:I need to find a function that is continuous at 0 but discontinuous at every other point. IV been stuck on this for hours now :( thankyou
ZaidAlyafey said:Continuous at just one point ! , then how does the limit exist ?
A discontinuous function is a function in which there is at least one point where the function is not defined or has a jump in its value. This means that there is a break or gap in the graph of the function, and it does not have a continuous line.
The types of discontinuities in a function include removable, jump, and infinite discontinuities. A removable discontinuity occurs when there is a hole in the graph of the function, a jump discontinuity happens when the graph has a sudden jump in value, and an infinite discontinuity occurs when the function approaches positive or negative infinity at a particular point.
A continuous function is one in which the graph has no breaks, gaps, or jumps and can be drawn without lifting the pencil from the paper. On the other hand, a discontinuous function has at least one point where the function is not defined or has a jump or break in its graph.
No, a function cannot be both continuous and discontinuous. A function is either continuous or discontinuous at a particular point, but not both. However, a function can have both continuous and discontinuous parts, meaning it is continuous on some intervals and discontinuous on others.
Discontinuous functions are used in real-life applications to model situations where there are sudden changes or interruptions. For example, a step function can be used to model the electricity consumption in a household, where there is a sudden increase or decrease in usage at certain times of the day.