Calc1131W3T2 - Formal definition of limit at infinity

Friday, 23 March 2018

1:29 PM

Machine generated alternative text: In the previous question you were given three values ot E and asked to find corresponding values of M _ Formalty, the meaning ot lim f(x) = L is that every > O there is a corresponding value of M such that M then If(x) —Ll < That's a lot ot M's to find' Fortunately, we can often do them all simultaenously by finding M as a function ot Lets conbnue the previous question where f(x) = e and formally prove the statement It we assume that x > M then -M We can make the right hand side e Note' the Maple syntax for In(l + e) is In lim = (b -M If(x) — Ll = < e E by choosing - IntepsiI•OJ1) 03 Pj
Machine generated alternative text: The spood ot a falling skyd.vor v(t) 42 (1 —e¯ in metres per second, wheret the number 01 seconds smce the plane Then the temnal veloclty L - lim v(t)- The distance IV (t) — Ll can besimplifved, as a function of t.to • . toget within rnetres per second or the terminal velocity is 2b metres per second of the terrrunul velocity go . to get Within 10000 Note Maple syntax exp(x) So the time it takes (to the nearest second) for the skydiver seconds 0 0 seconds
Machine generated alternative text: Suppose that tho avorago ATAR 01 a NSW high school student 's A(t) Whoro is tho number Of hours spont studying por wonk and A(t) — 100 (1 -e- Compute the number of houts of study per week required to enrol In the tollomng UNSW courses. Cive your answers rounded to the nearest hour • Bachelor 01 Alts, which has un ATAR 01 SO, requires ut least O hours 01 study per week . Bachelor ot Computer Science. which hus an ATAR ot 91. requires at least . Bachelor of Advanced Mathematics, which has an ATAR ot 97. roquiros at toast 1 ' 0 hours 01 study per weak hours 01 study per wook Anv grada ot more than 99.975 gets rounded up to a perfect ATAR 01 100 Assuminq tho formula is correct. how many hours of study per week are required to achieve a perfect ATARQ 0
Machine generated alternative text: the The Iin•vt 0t function as Infinity NOW prove thts us-ng the formal definita•. Of a Given e > O assume > M 1 S.rnpldv If(r) — Ll m termsotx If(z)- LIZ 0 Sance M can be large we assume that M > 2 Then 2 Use assumvbon that z > M to an tx»und on — Ll •n terns of M If(t) - Ll 3 Choose M so that your answer •n Step equals e Repeat the above fot A torrnal prod 01 statement s as any > O M > 3 then Note the MapJO IS the ts lg(x)

 

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