Limits Part III. Limits at Infinity. See the Description below for details.

0:00 Calculus I Limits Part III Watch my other video: Limits Part I at https://youtu.be/aqs2IB28SW4 and Limits Part II at https://youtu.be/75FzRUC48Ng Limits at Infinity. End Behavior. Vertical Asymptote. Horizontal Asymptote. The Squeeze Theorem. Slant Asymptote. [Using Long Division]. Introduction with the limit of x^n when n is Odd and when n is Even as x approaches infinity. End Behavior.

5:10 Example, y = [( 2+( 1/ x^2)]

6:44 Example, y = [ 5 + (sin x / sqrt (x)) ]. Using the squeeze Theorem.

10:37 Example, y = (3 x^ 4 - 6 x^2 +x -10 ). Using the Leading Term Concept.

12:23 Example, y = ( - 2 x^3 +3 x^2 -12 ). Using the Leading Term Concept.

14:13 End Behavior of Rational Functions. Example, y = ( 3 x +2 ) / ( x^2 -1).

17:07 Example, y = [ 40 x^4 + 4 x^2 -1 ] / [ 10 x^4 + 8 x^2 +1 ].

18:36 Example, y = [ x^3 -2x +1] / [ 2 x +4]. 20:44 Summary.

22:16 Slant Asymptote [Using Long Division]. y = [ 2 x^2 +6 x - 2] / [x + 1].

25:07 End behavior of exponential functions, Logs, Sine, and Cosine.

28:40 MORE EXAMPLES. Horizontal Asymptote. Vertical Asymptote.

The Limit from Right and Left using a graph.

Limit sin 3x over x as x approaches zero.

Limits Part II. Infinite Limits. See the Description below for details.

0:00 Calculus I Limits Part II Watch my other video:

Limits Part I at https://youtu.be/aqs2IB28SW4 and

Limits Part III at https://youtu.be/I7GO24j0W2g Infinite limits as x approaches a: Vertical Asymptote. Holes in the graph. Examples with Graphs.

1:02 Introduction: Lim of (1/x) and Lim of (1/x^2) as x approaches 0.

5:43 Summary of some graphs.

7:31 Example, y = 1 / (x-5).

8:30 Example, y = 1/ (x^2 +3).

10:48 Example, y = x / ( x^2-1)^2

13:42 Example, y = (x-2) / [( x-1)^2 ((x-3).]

18:17 Example y = (2-5x) / ( x-3).

20:23 A very interesting Example y = [x^2-4x+3] / (x^2 -1). Covers holes in the graph and Vertical Asymptote.

25:34 Summary of the previous Example.

27:53 Example y = x/ ( x^2 -2x-3)^2.

30:29 Quick Example paying attention to the positive sign and the negative sign to determine if the limit is positive infinity or positive infinity.

31:11 Example y = 1/ (x-2).

32:35 Example y = [ (x-1) ( x-2)] / (x-3).

33:31 Example, y = (x^3 -5x^2 ) / (x^2 ).