Solutions to Exam 2, take-home portion, Ma123, F05

# Calculus (With Analytic Geometry)(8th edition)

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 123 Calculus l Take-Home Portion of Exam II Rules: Work alone {i.e. without the heip of others} but use any reference materials antlfor technologyr you fincl useful. if the problems are unclear to you see your instructor [only] liar clariﬁcation I. An outﬁelder throws a ball at 84 tniiese'hr = ill? ﬁr'sec at an angle :9 above the horizontal: _—-'—'_ _'*-.. "it Me. may 9mg :13. W m isms; Museum '7 (Li I on tttl a. it~ the release point is 6.5 it above growtu, what angle ﬂ maximises the distance the hull travels”? {ignore air resistance} Express your answer in degrees. b. How the does the ball travel in the honacntai direction, assuming the ﬂight is not intpctlctl in any way? {Again i gnorc air resistance} c. The [1i ght ot" the ball (ignoring air resistance} thatr be described by what geometrical - a cune. Fa i (Note: Don’t make this problem harder than it is - use the javelin handout discussed in class and any,r formulas that appear on it to quickly work parts a. and b.} t I; it ‘ m we. 1) J 1 cams-ems) 2: 44.51? l §:?1Lr r"—————_n_—-——‘-I—l-- a .2. a = L?— J {2111+ 1(3'1)(£L§) : '51.. ffo.’??e. H I For the baseball purists, I realise that it‘sbettcr to "hit the cutoff titan" since the real goal is to get the ball itt as cutest}! as possible. 2. Teams A and B play in the World Series. By convention the ﬁrst team to win 4 games wins the WDI‘ld Series [it’s often referred to as a ‘best ofseven‘ series}. Suppose team A beats team 33 in each individual garrth with probability 3:. Then the probability that team A wins the lit'ort’eT Series in either a‘ or 5 games is given by {trust me} 5.x“ —4_r5 in this problem, your goal is to ﬁnd the value of the ﬁrst probability {3:} to make the second probability — the chance A wins the 1v‘r'orld Series in 4 or 5 games - equal to il.?5. That is. you are attempting solve the problem fix} = 5x' — 4s" — tits = e where .r is necessarily between [t and l . a. What is fﬂl)? What is ﬁll“? it What theorem {give a name} guarantees that there is at least one I between ll and 1 making fix) = it? You will need to use part a. to answer this question. c. 1liltihy is therey'trst one I for which ﬁx} = ll? (Hint: Give an explanation wltieh uses the derivative oi: f and the Fact that x. a probability. is between t] and 1.] d. Use Newton’s method to ﬁnd {approximately} the value oi" .‘t' making _f'{x]=tl. Continue using Newton‘s method {you get to choose the starting pointjl until subsequent values agree to at least three decimal digits (Le. they agree to llﬂﬂl}. Please list the sequence of values I: .1’2 that you generate. @ \$9): #555 {i (it’ll): {prod-5‘ @ ﬂﬂdm '7C [IL-5 {MW as. (0)13) (9 gECﬁJﬁE first): Slog—213mg: %x3(t-¥)abj (C t5 taco-wag I The baseball fans among you may object to this assumption {because the outcome is affected by a number or" variable factors including the particular pitehcrs playing a given clay1 the location of the game1 etc} but let's keep things simple here and try a ﬁxed chance of winning as a ﬁrst approsiniation. 3 Since team It is going to win the series in 4 or 2'1 games with chance 035 this might suggest how to choose your starting point. Should you start with an initial guess ofless than ELS or greater than [1.5.- for example? T) ﬁ-DIN "FINE 59% M Nﬁrm‘e— 5 WE ’1'. NH ﬁg JLJ {PIN @ “1 ﬁx- J \$ 0?; .— frxh Eh .— m 49 t 4 .. H in “KPH: 5 .. Wm RXth “ 3 3 052.10??? = ’g \$13é3 7ft. '39 K3 7' E3 2? \$9236 _F W4 "A f OD rd “131: w I (I?) K fur 'T‘f 6Wﬁ m hAN 6L QM fﬂt 3» I5 foé ?C: 3. Verify, using a computation dune by haan ihat J' I 3,,dx=~I-{I+2.x-}“+ I v}: {1+2x] * 2 {His-1" L [Q4— 1nf'“ + U.» 'foh‘] 4- c; 1 59* Ek- ’ '3' .— J. .— l “('11 ' z liculx) l 1 (“I”) is f l 1.. J, (w. ﬂ '2. (pg-Lg!“ (44413) 6. 1 l far-1r H I - 3*,» 1; 2 04-1101 0+1?) *1 .. 7f ((+LT>2’L ,u ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern