Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs

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Presentation transcript:

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Does not exist number number

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Does not exist number number

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Note:

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Example: Example: 1 0.1 10 0.01 100 0.001 1000 ------ ----- 0.000001 1,000,000 1 0.01 10 0.0001 100 0.000001 1000 ------ ----- 10^(-12) 1,000,000

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Limits at Infinity of Rational Functions To evaluate the limit at infinity of any rational function, we first divide both the numerator and denominator by the highest power of that occurs in the denominator. Example: Example:

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Remark: To evaluate the limit at infinity of any rational function, we first divide both the numerator and denominator by the highest power of that occurs in the denominator. Example: Example: Example: Remark:

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Notes: Notes:

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Example: Example: Example: Example:

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Notes: Notes:

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Exam-1 Term-151

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Example: (ex80p116) Multiply by conjugate radical. Example: Example:

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Horizontal Asymptote & The line Is a horizontal asymptote

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Example: The line Is a horizontal asymptote

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Example:

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs EXAM-1 TERM-121

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs b

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs To evaluate the limit at infinity of any rational function, we first divide both the numerator and denominator by the highest power of that occurs in the denominator. Multiply by conjugate radical. Factor then take the limit

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Example:

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Example: Example:

Postpone to sec2.6: Limits at Infinity: Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS Postpone to sec2.6: Limits at Infinity: Limit from one side does not exist Find an example for a function such that the limit from right does not exist

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Example: Example:

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Vertical Asymptote Horizontal Asymptote

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Who is going faster to infinity Example:

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Example: Sketch the graph of

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Factor then take the limit Sandwich thm high pwr in denomi Rational func Containing radicals Remove the | | Containing absolute value Multiply by conjugate radical. Containing noninteger Use Use graph Use

Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Reminder: After sec2.5 continuity