Asked by Janet
Find the discontinuities of the given function. Classify them as a point discontinuity or a jump discontunuity.
g(x)= x, x<-3
5x/(x^2-4x), x>= -3
g(x)= x, x<-3
5x/(x^2-4x), x>= -3
Answers
Answered by
MathMate
Evaluate g(x) at points close to the discontinuity:
Lim x-> -3<sup>-</sup> g(x) = -3
g(-3)=5(-3)/((-3)^2-4(-3))
=-15/21
=-5/7
So there is a jump from -3 on the left to -5/7 on the right.
Can you suggest what kind of discontinuity it is?
Lim x-> -3<sup>-</sup> g(x) = -3
g(-3)=5(-3)/((-3)^2-4(-3))
=-15/21
=-5/7
So there is a jump from -3 on the left to -5/7 on the right.
Can you suggest what kind of discontinuity it is?
Answered by
Janet
I assume it's a jump since it jumps from one value to another.
Answered by
MathMate
That is correct.
If you do not have clear definitions of each type of discontinuity, you can check the following link:
http://en.wikipedia.org/wiki/Classification_of_discontinuities
If you do not have clear definitions of each type of discontinuity, you can check the following link:
http://en.wikipedia.org/wiki/Classification_of_discontinuities