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Multiple Chaise
{3233,3132 choice that best (Templates Ilse statement 0:" answers the quesners
1. A ditrisicn c f Dittcn Industries manufactures the Futura mc de1 micrcwatre even. The daily:r cast (in dcllars) cf
prcducing these micrcwaire evens is CU) =
Justify all work using complete sentences .1 Use only methods from class.
F(><)
1. [12] a) Let x) be defined by the graph given above. Determine the following limits, writing +00 or -oo as appropriate. If a
limit does not exist, explain why.
Iim f
Volumes of Solids of Revolution
The volume of a slice is the area of the slice multiplied by the
width of the slice. vi : (area of side of slicei)(widthi ). The total
b
volume will then be: V Z L A dw .
We are going to examine slice perpendicular to the a
1. Prove that an equiangular triangle is equilateral (all sides are congruent).
By the Converse to the Isosceles triangle theorem if in AABC we have that 4A 3 AB
then BC E AC. Since the triangle is equiangular, we also have that 4A E AC from
which it foll
0.1. ARBITRARY CURVES l
0.1 Arbitrary Curves
We have shown that all regular curves can be parametrized by arclength, but to explicitly
do this for all curves is impossible, due to the nature of the functions involved. We will
need to modify the Frenet for
4.5 A Formula for Gaussian Curvature
The Gaussian curvature can tell us a lot about a surface. We compute K using the unit
normal U7 so that it would seem reasonable to think that the way in which we embed the
surface in three space would affect the value
1. (a) The picture is
The inner circle has radius 1, the outer has radius
Tr w/i
f/IQH dA 2/ / (TCOSQ)2(T81116)T d7" d6
'rr/2 1
R
(b) No picture was requested. The answer is
7T/2 'rr/2 ~3
dV:/ / / pcosqpgsingb dpdgbdQ
D 0 'rr/4 0
2. (a) We have our pi
Exercises 6.2
1. R is the region bounded by the graphs ofy : x2+l, y I 0, X I 0, X I 2. Let S be the solid of
revolution generated by revolving R about the X-axis. Find the volume of S.
Volume ofS =H-E(X2 +1)2dx= H-EGC" +2.7C2 +l)dt
l 2
=H- 7x5 +7x3 +x
Which 0F the Following represents +he Cartesian equcon 0F fhe parametric equarians
x = corsair) and y = 5cost'lfJ3 For 0 a r <15?
r a. y=-5:x-ng23
E: + 3f?
r . _
b 5"] 5m
@- c. y=5m1lm3
r d. y = Lam112
Ix+31m
r e. y=+1
51E
ix+3lm
r f. y=~1
S
lte_ Salve Fo
PreCalSection2.3Page 1 of 9
Math 1330
Section 2.3 Rational Functions
A rational function is a function of the form
r(x) = PW)
QOC)
where P(x) and Q(x) are polynomials.
The domain of a rational functions in the set of all real numbers EXCEPT the values o
1) The angle [in degrEESJ loaded a+ ver+ax A of u: +riangle ABC.
wifh verfices N6, 9, 51, BM, 6, 51 and (:15, ~51, 81 is
r a. 35.0713
1* In. 23.1431
r c. 63.9969
(3 11. 42.9221
r" e. 71.0219
r f. 47.0?9
Note: The law of cosines i5 fhe aasles+ way fa Find