Chapter 2: Limits and Derivatives.
Chapter 2: Limits and Derivatives.
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.