Download Answers Key for Final Exam - Calculus with Analytic Geometry III | MATH 3A and more Exams Mathematics in PDF only on Docsity! Math 3A Fall Quarter Final Examination
December 11, 2007
NAME: Ansuser Keg a Maw A S$ chem
TA & DISCUSSION SECTION: ~
You have three hours in which to complete this examination. Attempt all of the questions
Note that you will not be awarded full credit on a question unless your answer
is clearly, carefully and neatly stated and explained.
Problem | Maximum Score
, Score
1 5
2 6
on
=
‘Total 35
op sin
1)@) Evaluate lim ——
()@) Evaluate gant Dain 26 — sind
| pt.
jon Su Ite SO
G20 2o,a9-Su Bad 4 Co gO - Coso
- lie, Cos @
6a
wa (4Ca26~ &F 6)
e270"
< a
“ 3
(ii) Evaluate Jim (vel/* — a)
Qeb. Ae
\ree ya = lr @ 7 Vet
1-7 80 (= e x) Ave x
aie eb) Ly
aL? ee —— vJa™ —- \ Pe.
Vee el
Lod
= \
(iii) If f/{a?) is continuous, f(2) = 0 and f’(2) = 7, evaluate
els. fim —
{ Sime gid 20, he Finan Diet 40 4 jhe foom ofo]
jin Gla+2e) + $lerse) OL tu Size sada Sarsd5 | Leb.
Pe rr L0 — al
\
'(2).3 + $'(a) 5
ai+ 35
= SG
R es. (4)(a) Find y! ifa? -ay+y? =3
Ladd a dre 3 | ab
=) Qe -y- xy’ + 24y"= ©
—_ ¢ z _ a ”
2 vais Sa Be | | ete
ay x.
3 es (b) Find all the points at which the tangent line to a? ~ 2y + y? = 3 is horizontal
Wee whan W- Que 0. ‘| | pe
. z 2
Sudestibahing, A = ax wks the eapation x ty = 3
we 2
oo - x (gn) + BHAx) = 2
ay Sr=3
\ pb.
= « =4l
J. he tan Lie a lerizental at +e \ ot
pou mo 2) and (-1,~2). ce
(5) Suppose that the derivative of a function f(x) is f(a) = (a + 1)(a - 3)%(2 — 8)" for
all values of 2.
Apes. {a) Find all the intervals on which f(2:) is increasing. (You must justify your answer.)
. ' G .
§ (x) vo Mavens, a lan, $' 6) 7 oO. | lf
Ue lave Hat 2M re ouly when %>B. vet
o's § (a) a2 Werea sind only on the val ervad, fe, eo)
\ t {b) Which values of z are ciitical numbers of f{2)?
The Cibical munleers of fh) ane | pe
=e -t, 3 , G :
2 pls. {c) Find all values of x for which f(a) has a local minimum. (You must justify your
answer)
£! ta) hamoea At pA Frew negative te posttee | iee-
onby ak ~-3.
2. £6) naa a tweak Mini rte oly at 2%, | te
a
(6)(a) Write down a formula for the surface area S of a sphere of radius r.
SG: Ane? | Apes
(b) A spherieal snowball melts in such a way that its surface area decreases at a rate of
lem?/min. Find the sate at which the diameter of the snowball is decreasing when the
diameter is 10 crm
Let x lente Hee Liameber of He duewleall. |
Then wt he aud Ae | pe
G=Az(iyy = ee
« AS. avx dx Leb
dt dh
Lhe Qa ho), &
ol (ie)
' dw. -l
d& gor
heehee ee diame of fo vnewleall x decceasng ala
woke ob Smt] ria.
OT
“
Lee.
