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Unformatted text preview: a) {7% ea m bej Sample Math 115 Final Exam“
Fall Semester 2011 o The midterm examination is on Thursday, December 15 at 4:30PM — 7:00PM. 0 Room assignments are the same as for the common midterm exam and will be an—
nounced in classes and posted outside the math ofﬁce (405 Snow). 0 Only simple graphing calculators (Tl—84 plus and below) are allowed for the common
exams. You will marl: your answers on both exam booklets and provided bubble sheets.
You are considered responsible to bring pens/pencils and a calculator to the common
exams. Pens or pencils will not be provided for you, and interchanging calculators will
be prohibited during the exams. o The common ﬁnal exam covers — Chapter 2: Sections 2.1, 2.2, 2.3, 2.4, 2.5, 2.6; — Chapter 3: Sections 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7;
— Chapter 4: Sections 4.1, 4.2, 4.3, 4.4, 4.5; — Chapter 5: Sections 5.1, 5.2, 5.4, 5.5, 5.6; — Chapter 6: Sections 6.1, 6.2, 6.3, 6.4, 6.5 o The problems below, all multiple—choice with exactly one correct answer, are intended
to be reasonably representative of what might appear on the actual exam, which will have 30 problems. (A) m (B) l @3323: (D);17 (E) None ofthe above 2. Suppose that = f($)2 +1, f(1) : 1, and f’(1): 3. Find F’(1). (A) 3 (B) 4 (C) 5 6 None of the above 3. The unit price p and the quantity 3: demanded are related by the demand equation
50 — p(3:2 + 1) : 0. Find the revenue function R : 50$ 50 cc :62 + 1
Q3/3172 +1 (B) $2+1 (C) :3? +1 (D) 50 (E) None of the above 4. Find the marginal revenue for the revenue function found in Problem 3. —100$ 1— x2 C m D 50(1— 3:2) (mm (Elm ()2—5 ()'($2+1)2 (E) None of the above 5. Find 3—: in terms of a: and y when a: and y are related by the equation sci/3 + 311/3 : 1. W t)” we” o 1:)” o (E) None of the above 6. Find % at point (27 2M5) when a: and y are related by the equation 3,12 — $2 : 16. (B) )5 (C) % (D) % None of the above
/— 7. Let f(:c) : The domain of f is
(A) (—oo,2) and (2,+oo) (B) (—oo,2] and [2,+oo) @—1,2) and (2,+oo)
(D) [—1,—I—oo) (E) None of the above
8. Let f($) : ln(2 — :12). The domain of f is
(A) (—OO=+00) (B) (0=+00) (C) (wood?) (—oo,2) None of the above 2 10. 11. 12. 1.3. 14. 15. 16. 17. Evaluate: lim(3;z:2 — 4) m—'r3 \(
(A) 3 (B) 5 (C) 4
(D) The limit does not exist (E) None of the above
Evaluate ling 15.
(A) 3 (B) (C) 0
(D) The limit does not exist None of the above
Evaluate (A) Mi (3)0 +1 (D) The limit does not exist None of the above (A)—1(B)0 1 (D) The limit does not exist None of the above $271 2:12—2' Evaluate lim fit—>1— Find the horizontal asymptotes of function : lﬁﬂ. 1
(A>y=1 =1 (curl (D) The function has no horizontai asymptotes None of the above Find the vertical asymptotes of function f(w) : (12:32. (A)i:——2—1 (C)y:0 (D) The function has no vertical asymptotes None of the above The line tangent to y = $2 — 3m through the point (1, 2) has equation (0)“: : (A)y:$—3 (B)y+2:(2$—3)(m—1) earl (D) 3/ — 2 : (2:3 — 3)(33 — 1) None Of the above Find an equation of the tangent line to the graph of y : 2:11:13: at the point (1,0). (A) [email protected] (C) y:(:L'+1)lnzr:
(D) 9 : (x — 1) lnm None of the above Find an equation of the tangent line to the graph of y = ln(a:2) at the point (2, ln 4). 2 (A)y:$+2—:ln4 (B)y:— m—2)—ln4 (C)y:g($v2)+ln4 a:( m
2 + ln4 None of the above
3 18. Find an equation of the tangent line to the graph of y : 52“”3 at the point (3, 1). (A)y:2e%‘3 (B)y=2m—4 (CD :233—2 (D) 3; : 2e2m_3($ w m) None of the above 19. Find an equation of the tangent line to the graph of y : 5‘32 at the oint 1 1 e .
P : (Aly‘§(w+1)+: (BM—sgmsipé (c) :_§($_1)+é (D) 3) : —2$8_$2($ — 1) + i None of the above 8 20. The absolute maximum value and the absolute minimum value of the function f :
in)? — Zﬁ on [0, 3] are absolute min. value: a g; absolute max. value: 2 — 2\/§ (B) absolute min. value: 0; absolute max. value: 3
(C) absolute min. value: 0; no absolute max. value (D) no absolute min. value; absolute max. value: 3 (E) None of the above 21. Find the absolute maximum value and the absolute minimum value, if any, of the function f(9:) : (A) absolute min. value: 0; absolute max. value: 1 ( absolute min. value: 0; no absolute max. value
I o absolute min. value; absolute max. value: 1
(D) no absolute min. value; no absolute max. value (E) None of the above 22. Find the absolute extrema of function = te‘t. 1
(A) absolute min. value: 0; absolute max. value: ~—
6 (B) absolute min. value: 0; no absolute max. value 1
(C),an absolute min. value; absolute max. value: —
e (D) no absolute min. value; no absolute max. value (E) None of the above 4 23. Find the absolute extrema of the function f(t) : on (1, 2]. (A) absolute min. value: 0; absolute max. value: 1n?
1 (B) absolute min. value: 0; absolute max. value: ——
e (C) absolute min. value: 1; absolute max. value: 2 (D) absolute min. value: 0; absolute max. value: c (E) None of the above 24. Let f(m) : @133 w— 232 + m — 6. Determine the intervals where the function is increasing
and where it is decreasing. (A) increasing on (—00, 1) and on (1, 00)
(B) increasing on (—00, 1) and decreasing on (1, 00)
C decreasing on —oo,1 and increasin on 1, 00
g
(D) decreasing on (~oo,1) and on (1, 00) (E) None of the above 25. Let the function f be defined in Problem 24. Find the intervals where f is concave
upward and where it is concave downward. (A) concave upward on (—oo, 1) and on (1, 00) (B) concave upward on (goo, 1) and downward on (1, oo) @concave downward on (~00,1) and upward on (1,00) (D) Concave downward on (—oo, 1) and on (1, 00) (E) None of the above 26. Let the function f be deﬁned in Problem 24. Find the inflection points, if any.
If.“ (EA) my) : (MW) 03) (m) : (5.1%)) (C) (m) = (Moi) (D) No inflection points (E) None of the above 27. Let f(.r) : e‘zg. Determine the intervals where the function is increasing and where
it is decreasing. _ (A) increasing on (—oo,0) and on (0, oo)
creasing on (—00, 0) and decreasing on (0, 00)
(C) decreasing on (—00, 0) and increasing on (0,00)
(D) decreasing on (—00, 0) and on (0, 00) (E) None of the above
28. Let the function f be deﬁned in Problem 27. Find the relative extrema of f. A) relative min. value: 0; relative max. value: 1 (B) 33110 relative min. value ; relative max, value: 1
(C) relative min. value: 0; no relative max. value (D) no relative min. value ; no relative max. value (E) None of the above 29. Let the function f be defined in Problem 27. Find the intervals where f is concave
upward and where it is concave downward. (A) concave upward on (—oo,0) and on (0,00) /\ (B) concave downward on (—00,0) and on (0, oo)
. 1
(C) concave upward on (—00, —%) and on (V5,
1 1
(D) concave downward on (—00, ——) and on (—, oo); concave upward on (— «2‘ v2.3
(E) None of the above oo); concave downward on (—— 30. Let the function f be deﬁned in Problem 27. Find the inﬂection points, if any. (A) (m) : (wan) m) : (—%,f(—%)) and (ray) = (ﬁrs?) (C) ($5111) : (_%af(_ (D) (33,33!) 2 (E) None of the above Elle 31. Let f(2:) : xln 3:. Determine the intervals where the function is increasing and where
it is decreasing. 1 1
—) and decreasing on (—,00)
8 (A) increasing on (—00,
e 1 1 (B) decreasing on (~00, ~—) and increasing on (—, 00)
e e 1 1 (C) increasing on (U, —) and decreasing on ( ,oo)
6 . e  . 1 . . 1
decreasmg on (O, E) and increasmg on (—, 00) e (E) None of the above 32. Suppose that f is deﬁned in Problem 31. Determine the intervals of concavity for the _——. function. ‘ (A) . concave upward on (0, 00) (B) concave downward on (0, oo) 1 1
(C) concave upward on (O, —); concave downward on (—, 00)
e e l 1
(D) concave downward on (0, concave upward on (—,00)
e (E) None of the above 33. Suppose that f is deﬁned in Problem 31. Find the inﬂection points, if any. (A) (may) 2 (—aff ll (Bl (rig):(1,f{1)) (C) (may) : (Eiffel)
(D) To inflection points None of the above 34. Find the derivative of function y : 331”. (Hint: use logarithmic differentiation.) 1 anm I ’91 : (in $)2 : a: mlnx y I xinm (D) the derivative does not exist None of the above 35. Find the derivative of function y = 101'. (Hint: use logarithmic differentiation.)
(A) ’: 10‘” ln 10 (B) y’ : 10I (C) y’ : 10"" inc (D) the derivative does not exist None of the above 36. 37. 38. 39. An open box is to be made from a square sheet of tin measuring 12 inches X 12 inches
by cutting out a square of side 3: inches from each corner of the sheet and folding up
the four resulting ﬂaps. To maximize the olume of the box, take a = (A)1 (0)3 (D) 4 None of the above A rectangular box is to have a square base and a volume of 20ft3. If the material for
the base costs 30 cents/square, the material for the four sides costs 10 cents/square,
and the material for the top costs 20 cents/square, determine the dimensions of the box that can be constructed at minimum cost. (See Fig. 1.) (C) xxmxhz2.5><2.5><3.2 (A) xxxxh:1><1><20 (B)? xxxh:2><2><5 (D) a: X a: X h : 3 X 3 X 2.22 None of the above Figure 1: Problem 37. Postal regulations specify that a parcel sent by parcel post may have a combined length
and girth of no more than 108 inches. Find the dimensions of the cylindrical package of greatest volume that may be sent through the mail. (In the answers, 7‘ is the radius
and .l is the length.) 35 36 37
(A)7"><l:—><37 “><.l=——><36 (C)r><l=~—><35
7T 7T 7T
(D) r><12§><34 None of the above
7T It costs an artist 1000 + 52: dollars to produce :1: signed prints of one of her drawings.
The price at which m prints will sell is 400N572 dollars per print. How many prints
should she make in order to maximize her proﬁt ? (A) 1200 (B) 1400 @1600 (D) 1800 None of the above 40. The differential of function f(3:) : 1000 is [W
(A) 1000 (13) 1000014; (0) ' (D) dm
(E) None of the above
41. Use differentials to estimate the change in m when :13 increases from 2 to 2.123.
(A) 0.083 (B) (.082 (c) 0.081 (D) 0.080
(E) None of the above 42. The velocity of a car (in feet/second) t seconds after starting from rest is given by the
function
m) : 2x/t (0 g 4 g 30). Find the car’s position at any time t. (A) gt” + c 4.4 4
u_t3/2 _ 1/2
3 (0) 3t +0 (D) gt”? None of the above 43. Evaluate f 28$) doc.
2 ‘ .
(A) 3x3” — 28:” (B gas/2 w 2e:C + C (C) 3x2” — 28"" (D) 3502/3 — 2e”: + C None of the above 44. Calculate ff (4221/3 + d (A) 49 B) 50 (c) 51 (
2 None of the above (A) 3/2 (B) 5/2 (C) 7/2 (D) 9/2 45. Evaluate ft? (1 — $daz (E) None of the above 46. Evaluate fme—xgdw. (A) _em2+c (B) —%e_$+C (c) (1—2m2)e‘12+0 (E) None of the above 47. Find the area of the region under the graph of function ﬂan“) : 332 on the interval [0, 1]. A
(A) g (c) 21; (D) (E one of the above 1
5 48. Find the area of the region under the graph of y : 1122 + 1 from a: : #1 to a: : 2. (E) None of the above 10 ...
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This note was uploaded on 03/15/2012 for the course MATH 115 taught by Professor Bayer,margaret during the Fall '08 term at Kansas.
 Fall '08
 Bayer,Margaret
 Calculus

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