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MA 223 Final Exam Practice Problems1. Find the slope of the line containing the points (¡2; 4) and (6; ¡3).A. 4 B. ¡7=8C.1/4D.¡8=7E.¡1=22. Suppose 280 tons of corn were harv ested in 5 days and 940 tons in 20 days. If the relationshipbetween tons T and days d is linear, express T as a function of d.A. T =5d +280 B. T = ¡44d +500 C.T =44d +60 D.T =60d +44 E. T =44d ¡ 603. When 30 orange trees are plan ted per acre each tree yields 150 oranges For each additionaltree per acre, the yield decreases by 3 oranges per tree. Express the total yield of oranges peracre, Y , as a function of the number of trees planted per acre, x,ifx ¸ 30.A. Y =4500+60x ¡ 3x2B. Y =13x +80 C.Y =150x ¡ 3x2D. Y =240x ¡ 3x2E. Y =900+3x ¡ 60x24. A manufacturer can sell dining-room tables for $70 apiece. The manufacturer's total costconsists of a ¯xed overhead of $8000 plus production costs of $30 per table. How many tablesmust the manufacturer sell to break even?A. 80 B. 267 C. 200 D. 20 E. 1365. If f(x)=px +1andg(x)=x2+7thenf±g(¡1)) =A. 0 B. 3 C.p7D.7E.p8+16. If f(x)=2xthenf(x + h) ¡ f(x)h=A.¡2x2B.2x + h¡2xC.2x(x + h)D.¡2x(x + h)E.¡2(x + h)27. The domain of f(x)=13px ¡ 1isallrealnumbersx such thatA. x 6=1 B.x>1C.x>0D.x 6=0 E.¡1 <x<18. limx!1x2+4x ¡ 5x2¡ 1=A. 1 B. 0 C. 3 D. ¡3E.59. limx!1e¡x=A. 0 B. 1 C. ¡1D.1 E. e10. Supposef(x)=½Ax ¡ 3ifx<¡13 ¡ x + Ax2if x ¸¡1:Find all values of the constant A so that the function f(x)willbecontinuousatx = ¡1.A. 1 B. 0 C. ¡1D.¡72E. No value of A.11. Find all open intervals on which the function f(x)=2x3¡ 3x2¡ 12x + 12 is increasing.A. (¡1; 2) B. (1; ¡1) C. (2; 1)D.(¡1; ¡1) and (2; 1)E.Noneofthese.12. The derivative ofx2+1x +5isA.(x +5)2x ¡ (x2+1)(x +5)2B. 2x C.(x +5)2x(x2+1)2D.(x2+1)+(x +5)2x(x +5)2E.(x2+1)¡ (x +5)2x(x +5)21MA 223 Final Exam Practice Problems13. If y =(3¡ x2)3then y00=A. ¡6x(3 ¡ x2)2B. 24x2(3 ¡ x2) ¡ 6(3 ¡ x2)2C. 6(3 ¡ x2)D. 24x2(3 ¡ x2)E.Noneofthese.14. The line tangent to the graph of f(x)=x ¡1xat x =2hasslopeA. 5/4 B. 3/4 C. 3/2 D. 0 E. 1/215. Find an equation for the tangent line to the curve x2y + xy3= 2 at the poin t (1; 1).A. 2x + y =3 B.3x +4y =7 C.2x +3y =5 D.5x ¡ 2y =3 E.5x +3y =816. After t years the population of a certain town is P (t)=50+5t thousand people. A populationP has an associated CO2level, C(P )=(pP2+1)=2. In 2 years (when t = 2), the rate atwhich CO2level is changing with resp ect to t will beA. 5=(2p5) B. 150=p3601 C. 30p3601 D. 30=p3601 E. 50=p360117. If yx2+ y3= x ¡ y: Then y0=A. 1 ¡ 2xy ¡ 3y2B. 1 ¡ 2xy ¡ x2¡ 3y2C. (1 ¡ 2 xy)=(3y2+1) D.(1¡2xy)=(x2+3y2+1)E. None of these.18. If the concentration C(t) of a certain drug remaining in the bloodstream t minutes after it isinjected is given by C(t)=t=(5t2+ 125), then the concentration is a maximum when t =A. 25 B. 15 C. 5 D. 10 E. 2019. If f(x)=2x4¡ 6x2then which one of the following is true?A. f has a relative max. at x = §p3=2 and a relative min. at x =0:B. f has a relative max. at x = 0 and a relative min. at x = §p3=2:C. f has a relative max. at x = ¡p3=2 and a relative min. at x =p3=2:D. f has no relative max. points, but has relative min. at x = §p3=2:E. None of these.20. The derivative of a function f is f0(x)=x2¡8x: Then at x =2,f hasA. an in°ection point B. a relative maximum C. a vertical tangentD. a discontinuity E. a relativ e minimum21. If f(x)=13x3¡ 9x + 2, t hen on the closed interval 0 · x · 4,A. f has an absolute max. at x =3andanabsolutemin.atx =0:B. f has an absolute max. at x = 4 and an absolute min. at x =3.C. f has an absolute max. at x =0andanabsolutemin.atx =4:D. f has an absolute max. at x =0andanabsolutemin. atx =3:E. None of these.22. The total cost in dollars to manufacture x unitsisgivenbythefunctionC =3x2+ x +48: Forwhat value of x is the average cost a minimum?A.4 B.0.17 C.12 D.6.93 E.162MA 223 Final Exam Practice Problems23. A display case is in the shape of a rectangular box with a square base. Suppose the volumeis 21 cubic ft and it costs $1 per square ft. to build the glass top and $0.50 per sq. ft. tobuild the sides and base. If x isthelengthofonesideofthebase,whatvalueshouldx haveto minimize the cost? Give your answ er to tw o decimal places.A. 3.04 ft. B. 2.41 ft. C. 3.74 ft. D. 2.24 ft. E. 3.36 ft.24. What is the area of the largest rectangle with sides parallel to the axes which can be inscribedin the ¯rst quadrant under the parabola y =4¡ x2? (Give your answer correct to 2 decimalplaces.)A. 1.15 B. 1.33 C. 3.08 D. 4.00 E. 2.6725. The radius of a circular oil spill is increasing at the rate of 3 ft/min. How fast is the areaincreasing when the radius is 4 ft?A. 24¼ft2/min B. 48¼ft2/min C. 8¼ft2/min D. 16¼ ft2/min E. 32¼ft2/min26. Use di®erentials to approximatep3:96. (Give your answer to 3 decimal places.)A. 1.989 B. 1.990 C. 1.980 D. 1.975 E. 1.99527. Water is °owing into a tank which is in the shape of a right circular cylinder standing on itscircular base. If the water is °owing in at a rate of 80 cu. ft. per min. and the radius of thebase of the tank is 4 ft., how fast is the water rising when the water is 10 ft. deep?A.¼5ft/min B. 5¼ ft/min C.50¼ft/min D.5¼ft/min E. 50¼ ft/min28. A manufacturer has been selling lamps at $6 apiece and, at that price, consumers have beenbuying 3,000 lamps per month. The manufacturer wishes to raise the price and estimates t hatfor each $1 increase in the price, 1000 fewer lamps will be sold each month. The manufacturercan produce the lamps at a cost of $4 per lamp. At what price should the manufacturer selleach lamp to generate the greatest possible pro¯t?A. $6.25 B. $6.50 C. $7.00 D. $7.50 E. $7.7529. A population grows exponentially (Q = Q0ekt). In 1960 it was 50,000 and in 1965 it w as100,000. What was the population in 1970?A. 200,000 B. 150,000 C. 250,000 D. 300,000 E. 225,00030. If 18x=p3, then in which of the following intervals does x lie?A. (0; 1) B. (¡1; 0) C. (1; 2) D. (¡2; ¡1) E. (2; 3)31. If y =lnp1 ¡ x2thendydx=A.1p1 ¡ x2B.¡2xp1 ¡ x2C.¡x1 ¡ x2D.12(1 ¡ x2)E.12p1 ¡ x232. The amount of a certain radioactive substance remaining after t years is given by a functionof the form Q(t)=Q0e¡0:003t. The half-life of the substance isA. 53 years B. 0.00435 years C. 333 y ears D. 231 years E. 167 years33. If y = ex2thendydx=A. ex2B. x2ex2¡1C. 2xex2¡1D. 2xex2E. e2x3MA 223 Final Exam Practice Problems34. What lump sum of money should be deposited in a money market certi¯cate paying


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Purdue MA 22300 - Final Exam

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