Math 124, Sect ion G , Winter 2017, Midterm II

February 28, 2017

Name_ So_f uh-'--·o_~_.5 _________ _ Instructions.

• There are 4 questions. The exam is out of 50 points.

• You are allowed to use one page of notes written only on one side of the sheet in your own handwriting. H and in your notes with your exam paper.

• You may use a Tl-30x IIS ca.lculator. Even if you have a calculator, give me exact answers. (2 1; 3 is exact, 0.7, 0.70 and 0.699 are approximations for the same number.)

• Show your work. If I cannot read or follow your work, I cannot grade it. You may not get full credit for a right answer if your answer is not justified by your work. If you continue at the back of a page, make a note. Please I BOX I your final answer.

uest1on pomts

1

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!. Compute !!Jl . nccessarv d:r for the following v · · iOU aI . iswers should not llll\'e more t I

(a) ,, points) ·' ~ Ji + "'' >an one fraction lin s· . , e. •mplify if

1·3 - 5 - '- ~e~x...t::t~+s-) () 1,-- -2 {11el"- - '.) 1 , 1+e~

2

;i~n t -r-JJJXtJ 21-

2· (12 points) Let

- x2 - 14 , - ~ l" < 5 f(x) - { x2

- 3x - 4 2

List nil tht> critical nm b f, x -r 51, 5 ~ x ~ 10. . . nununum \"8lues of the continuous functio~ ;(rs) or ~(x) and find the absolute . x on its domain l-2 !OJ maximum and absolute ..

5 z:t<JO

?_ x -~ -~ 7 J.X - I~ :- -4

;:_ -y_ - ~ -= D vJ W (\ 1. ~ 3);_ (\" X. -\ L1 -:: 0 u, u,1 \'\ J{ - 7

cN~ 5, 3);__ ,1

i\ -l F j;.) \ -b

3

~ o f 1') Y\ o \ d,t,\ \-{"-AA ho 'olL td X-=S-

1 2__

3. The point (2 0) · ' is on the curve given by th . e equation

0 -

J_ 4

4. (11 points) In my dream, I am watching the men's final in Australia Open from a really nicf' court­side seat, 24 feet from the side line, in line with the service line, as shown in the picturf'. All the measurements are in feet.

j4-21Yjf- t8' ~j+.-21·--.1.- 2 1'-+ l+-18'-+ I +.. 21·-.1 ·

I r4

slltyWie

1N "

4 F :i !

36' 27' ~· • centtr mart:

1 1 f

....... 121·

ooe

T 24'

1

~-i N ------ 4'-------

\ \ \

\ \

\~ \

E

24t ~b t-')J )... lf

-:-L/(.l~

Actual dimensions of a tennis court and the positions of Federer, Nadal and the spectator.

A simplified diagram of the path of the ball B and the line of sight of the spectator.

Federer and :\"adal are both standing on their respective base lines, half way between the center mark and the alley line as shown, directly opposite each other. Federer hits the ball and sends it tO\\·ards Nadal at an astonishing 147 feet per second. As I try to watch the ball. how fast should my head be rotating, in radians per second, as the ball flies over the net?

d1: ~ l41 ft-/sec. cit

(I 41) 2376. 56~) 2g' 11. 56~~

Av QI 51/ - rad /sec.

5