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Calculus I - Final Exam 1 with Answer Key | MATH 115, Exams of Calculus

Material Type: Exam; Professor: Li; Class: Calculus I; Subject: Mathematics; University: University of Kansas; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 09/17/2009

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koofers-user-kmj 🇺🇸

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Exam 1 Math 115
Nu,,,., A r.+tnxr Ke-Y
KUID: -
Instruction: Solve
the following
problems
according
to the requirements and
show the
key intermediate steps
to receive full credits. You may use
your calculator,
but neither
books
nor notes.
1, (10 points) Find the
domain for the function
f (r): #
{f I 7r o
r(+
I
- I "t o '|
ry7/_l
2. (L5 points) Find
S-L
+o
"{+> f
x, btr.t 4 + 2
[-l
,2)Utt,+b)
l*o
=[a
I
= _rq
+>
I
z-J
L
pf3

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Exam 1 Math 115

Nu,,,., A r.+tnxr (^) Ke-Y

KUID: -

Instruction: (^) Solvethe followingproblemsaccordingto the requirementsand showthe key intermediatestepsto receivefull credits. You may useyour calculator,but neither booksnor notes. 1, (10 points) Find the domainfor the functionf (r): (^) #

{ f I 7 r o

r ( + I - I " t o ' | r y 7 / _ l

  1. (L5 points) Find

S - L + o

f x ,^ btr.t 4 + 2

[ - l , 2 ) U t t , + b )

l * o

= [ a

I = _rq+>

I

z - J L

  1. (15 points) Let f(r) :^ 2r5 -^ 3r2 + |r. to the graphof f(n) at,r:1.

f r c x y = 5 , z x + - 2 ' z l + t

9- 2-

Findtheequation .';:ff;r":" U- t - * - ) =

[ ] , - \ t q +-d * 5

b i t t i. - ^ Q \ o L [ 4 6

beCp'^-" (^) -9 *"

t l , + t r l )

i )

t )

  1. (10 points) Determineall valuesof r, for which f (") :^ ## is coutinuous. . a - - 5 7 1 6 = o (^) 5 ' * - w ) < , * ^ ) # h - , , , 1 ,a i r , )
  • z ) ( a - ) ) r e r l a '^

x i s^ r " ;^ +^ b t ' * ; 'a f > ' 3 )

t x = 2 , 3 Y f ( - e o ' : ) \ J ( ' ' \ ) U ( 3 ' t e o ) &*l,iS c--r.rfinraw5we'{A6l'4re'<l<'Et'a''t

  1. (15 points) The grossof domesticproduct(GDP)of a certaincountryis prljected^ ry = 2 ,^1 to be

t now? Ltry's(

billion dollarst yr from now. (a) How many dollarswill be the GDP 3yr from (b) What will be the rate of changeof this coun

( u t (^) N ( t ) = 3 ) ' + > ( g t t F '

l / ( t ) : t 2+ 2 t + 5 0 ( 0< t S 1 0 )

r $ r f ' ( t ) =^ 2 t +^

z

N ' ( S = 2 ( Q l +

  1. (10 points) Beiow^ is the graph of /(r). is differentiableat r: 1? Explain your reasoning. ye\ (^) fc*)i.S C,s^\i^ru"ot";to-t4=l

c^A{ Vre*VS^ t'a{Aa.0^ 2L

-- \

0

/(r) continuousat r^ :^ 7? Is /(r)

bgco,rrr.s-+fu-re- are- ,^^ l'- t-;

O (^) A,,D t.^ ) .i.5^ no'f^ oti"[tatt'*t-b tc-^ ,.-t q' -- |

C an^ nuL {{n^J^ ^^ t'{tT€"n+ [rnr,.e iS^ a.^ tofwr^ a-t^ ,L

l^ro- Lrure t^ ? \ )