What is jump discontinuity in math?

Answer 1

A jump discontinuity is when a function "jumps" from one value to another value at a point.

Define a function #f#. There exists a jump discontinuity at a point #a# if #lim_(x->a^-)f(x)=alpha# and #lim_(x->a^+)f(x)=beta# such that #alpha# and #beta# are real numbers (excluding #+-oo#) and #alpha!=beta#. An example is the signum function #sgn(x)=|x|/x# at #x=0#. Since #lim_(xrarr0^-)sgn(x)=-1# and #lim_(xrarr0^+)sgn(x)=1#, there is a jump discontinuity at #x=0#.
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Answer 2

Jump discontinuity in math refers to a type of discontinuity that occurs when a function has a sudden, finite change in its value at a specific point. At this point, the function "jumps" from one value to another without any intermediate values. The function is not defined at the point of the jump, and the left and right limits of the function at that point are not equal. This type of discontinuity is characterized by a gap or hole in the graph of the function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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