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Unformatted text preview: Math 16A (LEC 003), Fall 2007.
Oct. 24, 2007. MIDTERM EXAM 1 KEY NAME(print in CAPITAL letters, ﬁrst name ﬁrst): ___________________4____________________
NAME(sig'n): __________________________________________________ _ ID#: ___________________________________ _ Instructions: Each of the four problems is worth 25 points. Read each question carefully and
answer it in the space provided. YOU MUST SHOW ALL YOUR WORK TO RECEIVE FULL
CREDIT. Clarity of your solutions may be a factor in determining credit. Calculators, books or notes are not allowed.
Make sure that you have a total of 5 pages (including this one) with 4 problems. Read through the entire exam before beginning to work. A;me TOTAL 2 1.
(a) A line has x—intercept (0,4) and slope —1/2. Find its y—intercept.
S —— Ll = ‘ Az X
"= — A ~ “L = L 2 ‘ 2
\/t\~L w 4 2 x A L x O J 2, X Li) X 8 (b) A circle has center at (8,0) and goes through the origin. Find the equation of this circle. 1 m (xx—8) + \x) = (043' =ék} (c) ,In addition to the circle from (b), consider the circle with center at the origin and radius 4.
Find all points of intersection (if there are any) between the two circles. x1+ 3” = 4L» 2 — 2
2. Consider the function f = :2 +5: whether the function has any vertical asymptotes. Determine also its horizontal asymptote and
ﬁnd any points where the graph of y = f intersects its horizontal asymptote. Then sketch
the graph of this function on which all obtained points and asymptotes are clearly marked. . Determine its domain and intercepts, then determine :DoMa/lu‘, {:9 X . Imam: (0/03/(770) Q—l x" vLX ‘0 )XOrLteB "No dwwvlckﬂl M dec'um'waj‘vr kw: we ans. ALL—1X _ L xiv—2.x = >811
X «1x =
X—a—i (~47 4 3. Compute the following limits. Give each answer as a ﬁnite number, +00 or ——oo.
cc + 5 (aims 351 = “W “E
Cx—SB (X‘3L'Lx—i >
(b) lim x_5x_1 = /OAM ,L "M 'W'm u
‘9
§ 1 :Htho x—ar xl—éx +6¢><+5L
, — C 'L ’\1
Q $> x > ’ 9AM M (x :3“: ____ m 35_;_}_W
x—vt (Kl)
33—6 : — 00 ., C“
CM>O>0¢33
x3_4 4  {it};
Wham = «9:; 4 4 e
X 3+ — + "5/; + 3:; 4. Consider the functions f(2:) = $75 + 2x + 4 and g(w) = 3m — a: — 1.
(a) Determine the domains of the functions y = f (as) and y = 3>mm «44: X20 (b) Discuss differentiablity of y = g(a:). \ \y H Zx—L , "it “>0; 6’
3": "l X  1L ) it, >< < O .
No’c W ALQL at x no , «A ‘W‘
Mvdrﬁm 4M W “Ngwi M “L? M 2) ' Diwuixﬁw m get) MILLQ gig ,
(c) A line .is tangent to the graph of y = f (9:) and perpendicular to the line a: + 3g + 7 = 0.
Determine the equation of this line. T x L 3;
m +2 3 Wharf, but? IL+2=3 25? a
.L =32.=_'1
2J1"
X: ‘2‘? J :<&J§>
(Mud 3—&‘=%<X~4¥>
3: 3x + 4% (d) Compute f(g 1) and g(f(1)) ()
3(4): ’1 Jj/CA) =1!
4 (3m) 1m :4 ) gym: ﬁn) : «g “WA,W~..._.~u “*M ...
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This note was uploaded on 06/23/2010 for the course MATH math16 taught by Professor Na during the Spring '10 term at UC Riverside.
 Spring '10
 NA

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