MATH 1044 Lecture Notes - Lecture 3: Petri Dish
Document Summary
To (cid:449)rite the e(cid:374)d (cid:271)eha(cid:448)ior as (cid:449)e had, e. g. as (cid:454) (cid:449)e ha(cid:448)e f(cid:894)(cid:454)(cid:895) 5, is a (cid:271)it (cid:272)u(cid:373)(cid:271)erso(cid:373)e. i(cid:374) math, we use more compact notation called limit notation: As you may have guessed, this end behavior of a function we have been discussing is one type of li(cid:373)it. I(cid:374) it"s (cid:373)ost ge(cid:374)eral defi(cid:374)itio(cid:374), a li(cid:373)it of a fu(cid:374)(cid:272)tio(cid:374) is (cid:449)hat (cid:448)alue a fu(cid:374)(cid:272)tio(cid:374) approaches (cid:894) and - are (cid:448)alid possi(cid:271)ilities here(cid:895), i. e. (cid:449)hat (cid:448)alues the ouputs approach, as the inputs tend to a certain value. To talk about the limit of the function, we need to know what value we want the i(cid:374)puts to approa(cid:272)h, i. e. or - i(cid:374) the (cid:272)ases (cid:449)e ha(cid:448)e (cid:272)o(cid:374)sidered (cid:894)(cid:449)e (cid:449)ill (cid:272)o(cid:374)sider other (cid:448)alues later). As we had seen, li(cid:373)its (cid:272)a(cid:374) (cid:271)e fou(cid:374)d fro(cid:373) a fu(cid:374)(cid:272)tio(cid:374)"s graph. Ho(cid:449)e(cid:448)er, li(cid:373)its (cid:272)a(cid:374) also (cid:271)e determined by numerical and algebraic representations of a function.
