Removable Discontinuity...1

[nycmathguy]

Calculus
Section 2.5

Before answering 25, explain in layman terms the idea of removable discontinuity. I need 25 (a & b).

Thank you.

 

[MathLover1]

Removable Discontinuity: A removable discontinuity is a point on the graph that is undefined or does not fit the rest of the graph. There is a gap at that location when you are looking at the graph. When graphed, a removable discontinuity is marked by an open circle on the graph at the point where the graph is undefined or is a different value like this. In other words, a removable discontinuity is a point at which a graph is not connected but can be made connected by filling in a single point.

25.
f(x)=(x-3)/(x^2-9).........note: you can factor denominator

f(x)=(x-3)/((x-3)(x+3)).........now you can cancel (x-3).........since (x-3) is zero that we have removed, at x=3 functions will be continuous, but f is undefined

simplyfy

f(x)=1/(x+3)

 

[nycmathguy]

Removable Discontinuity: A removable discontinuity is a point on the graph that is undefined or does not fit the rest of the graph. There is a gap at that location when you are looking at the graph. When graphed, a removable discontinuity is marked by an open circle on the graph at the point where the graph is undefined or is a different value like this. In other words, a removable discontinuity is a point at which a graph is not connected but can be made connected by filling in a single point.

25.
f(x)=(x-3)/(x^2-9).........note: you can factor denominator

f(x)=(x-3)/((x-3)(x+3)).........now you can cancel (x-3).........since (x-3) is zero that we have removed, at x=3 functions will be continuous, but f is undefined

simplyfy

f(x)=1/(x+3)

Let me see.

After factoring the denominator of the original function, the result is 1/(x + 3). We have removed the discontinuity at x = 3 because (x - 3) was canceled. In other words, we filled in the hole making the function continuous at x = 3. Yes? Still, I don't understand why the function is undefined. Are you saying the original function is undefined?

 

[MathLover1]

yes, we filled in the hole making the function continuous at x = 3
the function is undefined because that (x-3) exists in given function f(x)=(x-3)/(x^2-9).

here is another example:

 

[nycmathguy]

yes, we filled in the hole making the function continuous at x = 3
the function is undefined because that (x-3) exists in given function f(x)=(x-3)/(x^2-9).

here is another example:

Thank you for the clip.