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Unformatted text preview: MATH 110 Test 4 October 29, 2009 Name: 30/1,: from 5‘ Section:
Instructions: Show all work. Partial credit will be given. 1. Find the inverse of the following functions:
a. f(x) = 1n (2x+2) (5 points) y: /n (2X+Z) 332x+i
8 —'i '
Bazzax igjjfx ‘X"§ (3)
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b. f(x)= e9x+6l5points)
jraqxv‘é
(éﬂe‘ix
jj" ’ 4‘ ‘,i/ .
Jgﬂ/‘jé)=9x 431557313 c x ”10 7)
c. f(x)= 1+21n (x—2)(5 points) (ﬂuI”? .
ﬂ" rig/“(#2) ‘ e “('1 
3.4 s 215064) afa”7/2+ ;,_¢><¢49“ (j) ”if/:5 : j/w (K’Z)
Z 2. Find a numberx such that e6x'5 = 3. (10 points)
£44. 3 : 67X’ Z"
ﬁmg+§¢éx 3. Find all numbers r such that ln(2r3 — 3) = ——1. (10 points) é’IZZFg”3 r5(eflt3)t/3
r; ’2 4. What is the area under the graph ofy = 1/95 from x = 1 to x = e? (10 points) ill/€61 {ZS 561) :«é‘mﬁ :/ 5. Find all real numbers that satisfy the following equations:
a. 1n(x + 4) — ln(x — 2) = 3 (10 points) 221 @1723)
(w In(15x) b' ln(2x) = 2 (10 points) A Kidh X c 2 “an slitW
yaw/r hme' "2 QMQMWX If
M‘xslgn/f’g/gml, : ﬂn/f’ﬂl} 997‘ 2?
x 61,5:
9" 6. Find all numbers if such that the point (3, t) is a point on the unit circle. (10 points) ﬁndi Wm. x = 3/; ﬁnvlmyecfs x143»; :/ : z . . l ,, i 4‘
g) *‘f’cl 3096’ «a
i r ""c/ Z;— g¢7ipﬂ ’“I/L’
9 z? 25’ 7. What angle corresponds to a circular arc on the unit circle with length % ? (5 points) a: £27,344: 19,71.“ so] Maw]??? ; {9 M {9: ITARX/XD :ls’
‘ " ﬂit) 77— 77 M77" 0 ﬂnoﬂw4 my 7% kaol’ 6er~ I“! ”j 5'; 50a; Sb 1 7‘ WXIi : 30911 7/5,”? * l7, “5 Z 8. What is the slope of the radius of the unit circle that has a 30° angle with the positive horizontal
axis? (10 points) The racism: P015 3&8 'Wovgj‘vx album" pointS (0,03 (mi (44%)32)‘ 3‘3)
M7 V147 : Vt “ J» t E 9. Suppose an ant walks counterclockwise on the unit circle from the point (1, 0) to the endpoint of
the radius that forms a 55° angle with the positive horizontal axis. How far has the ant walked? (10 points)
[ﬁg 111‘]: ‘9' 7r 3 5’??—
W 7370 f Y0 10. Extra Credit: The circumference of a circle of radius r is 21m“. What is the length of a circular arc
corresponding to an angle of 9° on a circle of radius r? (10 points) «’Z’Mﬂ’ ﬂat/hm 6f ﬂirt/e MVP/W )C CircumMncz. a"; (WC/f.
5 j.— x 277/ 360 3 £17:
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 Spring '09

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