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**Unformatted text preview: **.---—--~:-.\__
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_ . Math _142 - Quizl if“ No calculators, Show all of your working. Name: ‘7 l' l 5 100+
5 1. Evaluate the indeﬁnite integral 1+4:1: ————————~—~—dm
v1+$+2m2 2. Evaluate the deﬁnite integral, if it exists: fan ‘1)25 dz: l‘l—l‘lx _ Ax V: \+>{+1xl
{i\+x+ml W = 3*le (M ,
r‘J W W : _..,.___.. .....
(I 25 \J'V" X=U w“:
\ L'X‘l) 5"? cl. " (”Wu x": l xvii"; I Math 142 — Quiz2 I No calculators, Show all of your working. Name: .' l 77 7' 743” \S‘Eetch the region enclosed by the given curves. QECide whether to integrate with respect
to a: or y. Biaw a typical approximating rectangle and label its height and Width. Then ﬁnd
the area of the region. I 1.'2:=1'—~y2,1::y2——1. RESPEH'TD x; Page 2 @ Math 142 — Quiz3 No calculators, show all of your working. Name: 1.4:... L EH, ) ’lOD . 1. Find the volume of the solid obtained by rotating the region bounded by the curves
y = 33 and y 2 J55 about the line y z 1. Sketch the region, the solid and a. typical disk
or washer. 2. Use the method of cylindrical shells to ﬁnd the irolume of the solid obtained by rotating
the region bounded by the curves 3; 2 $3, :4 : 8 and a: = 0 about the zit—axis. Sketch the region and a. typical shell. .’1 ,- L
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the work done. W" l: Cl Cl : SODH . b l‘ “N; a . '1, goo 14*: ‘7."-
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Tt - 50 14 ———
(t )- + sin 12 Find the average temperature during the period from 9am to 9pm. 1 b . 5’ 3 ll
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‘1 m M \“J Page 2 Math 142 — QuizS I No calculators, Show all of your working. Name: _ _ '2‘ 700 1. Find the formula for the inverse of the function f($) : v10 — 31' 2. Suppose g is the inverse function of f and f (4) = 5,f’(4) = §. Find g'(5). I143"? ISLQ):4 ,
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No calculators, Show all of your working. Name: __._._'_\A - 1 Mb 1. Find the derivative of y = cos—1(ezz). Simplify if possible. l5: CM" LELXB
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Name: ww—ﬁ—“—_ 1. Evaluate the integral [0035(33) sin4(m)d2: 2. Evaluate the integral U: 90315343
f moswmdm {A 53,47: n By. on;
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‘__.__..— Page 2 Math 142 - QuizS No calculators, show all of your working. 4 Name: 1. Evaluate the integral using the indicated trigonometric substitution. Sketch and label
the associated right—triangle. 1
——-——-~———d$ 1::33eczz:
21/ 2_9 ’
m 33 x1: amtx
ox: . \
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do: gtcx mﬁx 0‘ x 2. Evaluate the integral x ‘J" xzﬂr
r” 91* (Aw- «m dx “Mr
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‘11 x}— Page 2 Math 142 — Quile No calculators, show all of your working. Name: _" , ' Maj H3004 - _ 1. Write out the form of the partial fraction decomposition of the function. Do not deter—
mine the numerical values of the coefﬁcients. (a)
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xq/
t4+t2+1 ’ pm» f“ o 4;"
2 2 2 : TEL—D « 3-"
(t +1)(t +4) 1
El ﬂag {ff-N)" 2. Evaluate the integral 1
——-——-dm
f m/ 4:1: + 1
(Hint: make an inverse substitution to make this into something for which you can use
partial fractions.) 1 U: LZIQM ul=uox1 m ‘1 EH : MU'D kPJLu’rD
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Ham-11 Wm H" ‘l We Math 142 — Quizll @ No calculators, Show all of your working.
Name: _._.._.._,__H. M 7 Cl '2 339‘ 1. Determine wether the integral is convergent or divergent. Evaluate it if it is convergent. 1
1
[002—de um “I. _ _I_ _
W" ’3 f2.——~U\j {w — O
@0meth 2. The integral [:0de is improper for two reasons: The interval [0,00) is inﬁnite and the integrand has an inﬁnite discontinuity at 0. Evaluate it by expressing it as the sum of two improper
integrals as follows: immdmfﬁi‘amfﬁdmde (Hint: you might want to use an inverse substitution to evaluate the integral... and you
should have an inverse trig function when you integrate.) a"; - ’1.
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