Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs 丌/3mx EXAMPLE Im(tan x) lim(tan x) x→ x→
lim (tan ) 2 x x→ + lim (tan ) 2 x x→ − EXAMPLE Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Does not exist number xaar(r ( number
f x L x a = → lim ( ) number Does not exist number + − Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Example: Example: Theorem: if r>O Find. lim Find lim x x→0 x→>y/ x x x x 10 0.1 10 0.01 100 0.01 100 0.0001 1000 0.001 1000 0.000001 000,0000.000001 10000010~(-12) lim 0 =0 X→0 X X→00 x
Example: x x 1 Find : lim → 1 1 10 0.1 100 0.01 1000 0.001 ----- ------ 1,000,000 0.000001 x x 1 0 1 lim x = → x Example: 2 1 Find : lim x→ x 1 1 10 0.01 100 0.0001 1000 0.000001 ----- ------ 1,000,000 10^(-12) x 2 1 x 0 1 lim 2 x = → x 0 1 lim Theorem : if 0 = → r x x r Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs Theorem: if r>O X→0 x Theorem: if r>0 m =0 X St x' is defined
s.t is defined 0 1 lim Theorem : if 0 r r x x x r = →− 0 1 lim Theorem : if 0 = → r x x r Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs