Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs number E xample Infinite Limits Find the limits in Exercises 37-48 2x 2x2+1 x →+3-x-3 44. lim 0x(x+1) E xample 45. a. lim 2 b. lim 2 →03 x→0 a)lm b)lin x→0 x→ x x 5x+2 2 a)lm 3(x-3) 2-5x lim x
0 = number lim 3 2 ) lim →3+ x − x a x 3 2 1 ) lim 2 3 − + → − x x c x Example: 2 0 1 ) lim x a x→ Example: 2 3 ( 3) 1 ) lim → x − b x 2 3 ( 3) 1 3 ) lim − − → x x c x 5 3 ( 3) 5 2 ) lim − + → x x d x 6 3 ( 3) 2 5 ) lim − − → x x d x Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Infinite limits (a)limf(x)=+∞ (b)lim f(x)=+oo r-a+ 0 0 (c)lim flx)=-o0 (d)lim f(x) r.d
Infinite Limits + + − − Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs y I. The graph of f is given (a) Find each limit, or explain why it does not exist (ii) lim f(x) (v)lim x→-3 x→0 (ii) lim f(r) (iv) lim f(r) (vi) lim f(r) x-)
Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Vertical Asymptote lim f(x)=too x→)a DEFINITION A line x= a is a vertical asymptote of the graph of a function y=f(r)if either imf(x)=±∞ or lim f(x)=±∞ x→a y (a)limf(x)=∞ (b)limf(x)=∞ (d)lim f(r)=-oo c) lim f(x)=-∝
Vertical Asymptote & = → lim f (x) x a Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Find all vertical asymptotes
Find all vertical asymptotes Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs