# How do you find jump discontinuity?

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 finitieIt 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)#

By signing up, you agree to our Terms of Service and Privacy Policy

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.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- How do you show the limit does not exist #lim_(x->4)(x-4)/(x^2-8x+16)# ?
- How do you evaluate the limit #sqrt(3-3x)# as x approaches #1^-#?
- What is the limit of #x^(1/x)# as #x->oo#?
- For what values of x, if any, does #f(x) = 1/((3x-2)sin(pi+(8pi)/x) # have vertical asymptotes?
- What is the limit of #[ ( t^2 + 2) / (t^3 + t^2 -1) ]# as x approaches negative infinity?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7