Continuity I

Sketch the graph of a function that is continuous except for the stated discontinuity.

Discontinuous, but continuous from the right at 2.

Continuity II

How can you eliminate the discontinuity of f? In other words, how would you set f(5) to ensure f is continuous at 5?

Continuity III

Use the Intermediate Value Theorem to show that there is a root of the given equation x^2+x-9=0 in the interval (1,2).

Limits Part IV. Continuity.

0:00 Limits Part IV. Calculus I. Continuity.

2:54 Continuity Checklist.

4:27 Example with a graph.

9:33 Continuity on an Interval.

10:31 Polynomials and Rational Functions.

11:37 Continuity at Endpoints. Left-Continuous and Right-Continuous. 14:38 Trig Functions.

18:19 Example, y = [2 x^2 +3x + 1] / [ x^2 +5x].

20:01 Example, Piecewise Function.

22:54 Example, y = [ x^5 + 6x +17 ] / [ x^2 -9 ].

24:21 Example, y = [ ( 2x + 1)/( x) ]^3 .

25:20 Example, Piecewise Function.

Continuity IV

Find the x-value at which f is discontinuous and determine whether f is continuous from the right, or from the left, or neither.

Limits Part V. Precise Definition of Continuity.

Precise Definition of Continuity. Calculus I.

Corrections, I started saying this is Limits Part IV, but it is Part V.

Covering the Precise Definition of limits with one example. To master the use of this definition, you will need many examples. I will keep that in mind in the future. So, if I make another video with this topic, I will call it Part II