2-2 LIMITS INVOLVING INFINITY. Let’s start by considering and y = 0 is a horizontal asymptote because Def: The line y = b is a horizontal asymptote of.

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2.2 Limits Involving Infinity

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2-2 LIMITS INVOLVING INFINITY

Let’s start by considering and y = 0 is a horizontal asymptote because Def: The line y = b is a horizontal asymptote of f (x) if Graph EX  y = 2 is a horizontal asymptote because

Ex 1) (look at graph; look at table) *Right & left sides were different – that’s ok! Note: The Squeeze Theorem / Sandwich Theorem works using  Properties of Limits as (1)sum(2) difference(3) product(4) quotient (5) constant multiple(6) power

Let’s graph again Def: The line x = a is a vertical asymptote of f (x) if either vertical asymptote at x = 0 Note: Frequently there is a vertical asymptote where the denom = 0, but not always! EX  so be careful!

End Behavior Model Ex 4) Graph window [–2, 2]×[–5, 20]; then window [–20, 20]×[–100000, this window  they look the same!

Def: A function g (x) is a a) Right End Behavior Model iff b) Left End Behavior Model iff Note: If Right = Left, we just say End Behavior Model Ex 7) top bottom simplify the end behavior model

The Right & Left End Behavior Models can be different! Consider: RLRL Right: Left: is the same as EX: We can also investigate difficult limits using reciprocals!

HOMEWORK Pg. 66 #10, 38, 41, 46, 50, 61, 71, 73, 74 Pg. 76 #1 – 52 (mult of 1+3n)