ame _

Recitation Section _

Math 103 (Spring 2010): Midt rm IThur day, ar h 2nd, 2010

1:30-2:20DRL 2

This exam has 6 multiple choice questions worth 10 points each and 2 open end d qu stions worth 15 pointseach for a total of 90 points. Partial credit will b given for th entire exam so be sure to show all work. Onthe multiple choice, circle the correct answer(s) and give supporting work, a correct answer with little or nosupporting work will receive little or no cred.it. Use the space provided to show all work. A she t of scrap paperis provided at the end of the xam. If you write on the back of any page please indicate th.is in some way.

You have 50 minut s to complet the exam. You are not allowed the use of a calculator or any other I ctronicd vice. You are allowed to use the front and back of a standard .5" x 11" sheet of paper for notes. Please silenceand put away all cell phones and other electronic device. When you finish. please stay seated until the entire 50minutes has lap ed. When time is up continue to stay seat d until someone comes by to colle t your xam.

I Problem I Points ~ Score I1 102 103 104 105 106 107 158 15

I Total 90 ~'--__

1

1. Find 1'(1) if

f(x) = (x ,+ 8)! _X3 +8

(a) -~ (b) -~ (c) -i ~ (e) i (f) ~ (g) ~ (h) ~

()(\(3-\-~)~)«((x:r'4~!'3) - (x-t~;)r~(f.'!C.(.r~,,'tS')-----~~--,.,....".,. .......~---~•........

( X.v'!. ~ )'1

t (')(''3 ~ ~ )( X-I- ~;3_~iZ4~-~------

f >(It!'; + <6 )'2..

NO\JJ e..I.TJ~ cd. x,~)

\ ('y." "'\ ( -)i/,! I -~ ( ~/"3 \ -\~) [+8" -~I l+8)!i------ ------------

( \ V'3 ..1;. 8")"1..

\

3-~

9.Q 3_~.

r-------·----1

I3

y'f !.- -. ,/~

3----;;;;;..---- ~

2

(C~1t\ Qwle -

" P~w.<4~~)

1-[(a) -4 (b) -3 (c) -2 (d) -1 (e) 0 (f) 1 l(g) 2 (h) 3

- 't!'2 t. LX cAe ~ t- ~2 4 2..~)

L.: -I 2?<- (_ 2 x-\- L)

d -tC.4-2..x .~ +-~x..

(--2><-~"L) ;:Jk e +- e, !.&-2-x-t L)

(f Y-oo\tt(:,"\r~.)

(c...~" 't~)

"2.. ~l.. ~. 0"* 2'0 -0 + l.: 6

(...:2'" 0 + z.J e - 2e

II 0 0(e - Ze =- 2_

3

3. If f(x) = sin3(3x), find f'({;).

(a) -9f (b) -3f (c) -1 (d) 0 (e) 1 (f) 3f ~"~J(h) 3)2

3 .s \N2 s x. ~(s n\) 3x)

4

4. If 3xy + y2 = X3 - 1, find the slope of the tangent line at the point (-1,2).

(a) -4 ~ (c) -2 (d) -1 (e) 0 (f) 1 (g) 2 (h) 3

\w-~XA <..~-t \)(~<M.~ ~\ ~_-l,--.~~"·'--""----~"""""""""~"'''l_'''.~

:= 3 j -tJ;<)' ~,~ ~ or Lj~,,-.- \,.+< • ..~ •••...•.

r:p n::J.,w:.,~ '(-~

"3 'j + 3K~')<: -t.- '2<:) ~x

So

A}tE

E.V'~.d:t ~ (- II '2..) "

z,3x- 3c---37<+2.'0

2-3(-1) - 3- 2.--~--3(-0-1-2· 2.

5

5. Let

f(x) = {x2 + 1c2 - 3cx + 3x - 1

if x 2: 1if x < 1

Circle all possible values of c that make the function continuous on (-(X), (0).

(a) -4 (b) -3 (c) -2 (d) -1 8 (f) 1 (g) 2 th)~

'5 i V\u... bo\1." ? ~!tS (X ~ \ O-M-J 'l( -c, \ -; (#f4!.

~~ \f\ \A. Q v ~ \-;~ ~'I.S4A¥\~ e ••.., .\~ \s. s~4t·c.(~ <\-,()

'vV\~ Svlf'€- ~ ~ 0-.; r~ D-Jt ~ \V\.~'~<J.

\~ ~ <..U o-v-J s I ~l

2..

\ -+- t -

'~ c,;:o)3

6

6. Evaluate

x"- \

X2 -1lirn .

x->-l )2 + x-I

~a) ~ (b) -3 (c) -2 (d) -1 (e) 0 (f) 1 (g) 2 (h) 3

::::<X:-l

.,f-z.+;; ~o

( XL_ \ ") Cfl::t X',+ l")••• _11. .........~~

1 '1....("2.-+>)<.) . \

._--._--X -to. ,

IN c:. tA) use. J,(f, c+ Sv\"'S,· liov>. ?Vb\J(,;f .'-1t,

(x. -l (/~ + \)

7

7. Let f(x) = In(x + lnx). Find the equation of the tangent line to f(x) at x = 1.

d~ ( ) \ (I ' I) -;;.. I- •..2~d - l.#-k. l -, =-2>< I

So sf~ W1.=.2.

Wb x::=- \, {- (1 ) ~ ~ (t -t L J) s: ~I.\ (/ +-0) ~A (()7:'"0,

-r1.~s ~ ~ jj.".-,.L ?a'S~'S~>..A..~.L.~?~\wt CI)b)

Pol~~ ~{~ h:,rYh:

~-o :: 2'(K-l)

:=?I [-S ~ 2~- ~

8

8. The base of a certain right triangle is held constant at 4 inches while the length of the hypotenuse isincreasing at a rate of 1 inch per second. What is the rate of change of the length of the third side of thetriangle when the hypotenuse is exactly 5 inches long?

-) a. (t) ~ ~(~t:))t~"ib-~do..--Cu::

\'2

2 c (~ ) ~de.c\l.

a l~) ~ './-5~,~ =- {2.r~-:j6.::;;.....jq - 3 il'\c-~s .

1.."2

9