Home > Calculus > Classifying Topics of Discontinuity (removable vs. non-removable)

How do you find jump discontinuity?

Answer 1

There are 2 ways, you can look at a graph or you can use the definition.

Using the definition, show:

#lim_(x->a^-)f(x)!=lim_(x->a^+)f(x)# and both are finitie
It is important that they are finite. If one is not finite or does not exist, then it would be infinite discontinuity.

Using a graph, it's the same thing; both the red and blue functions have jump discontinuity:

Let's say the red function, #f#, is discontinuous at #a# and the blue, #g#, at #b#. Notice:

#lim_(x->a^-)f(x)!=lim_(x->a^+)f(x)# and #f(a)# #DNE#
#lim_(x->b^-)g(x)!=lim_(x->b^+)g(x)# and #lim_(x->b^-)g(x)= g(b)#

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Answer 2

Emily Ammerman

To find a jump discontinuity in a function, you need to examine its graph. A jump discontinuity occurs when there is a sudden, non-removable gap or jump in the graph. This means that the function has different values on either side of the gap. To identify a jump discontinuity, look for points on the graph where the function approaches different values from the left and right sides. These points indicate the presence of a jump discontinuity.

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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.