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國立嘉義大學 102 學年度基礎學科學力競賽試題卷: 科目: 經濟數學 1. Each unit of a certain commodity costs p = 47x + 12 cents when x units of the commodity are produced. If all units are sold at this price, express the revenue derived from the sales as a function of x. A)46x + 12 cents C) 48x + 12 cents D) x(47x + 12) cents B) 47 x 2 12 cents 題型:選擇題(共 25 題) 0 is A) 配分:100% y = 5x + 1 B) y = 5x – 1 f ( x) f (t ) x 1 x3 A)all real numbers x except x = 1, x = –1, and x = –3 B)all real numbers x C)all real numbers x except x = –3 D)all real numbers x except x = 1 and x = 4 f ( x) 2 8. What is the rate of change of 9 19 A) 4 B) 4 C) 16 x 2 3x 2 lim x 1 x2 1 B) 6 C) 3 2 A) D) 3 1 4 10. Find f ( x) A) f ( x) C) 2 D) –2 B) f ( x) 5. List all values of x for which f (x) is not continuous. 2x 1 f ( x) 2 x x . A) 1 2 D) 0.0006 7t 5 t 2 with respect to t when t = 2? 17 D) 4 selling 4 per day. C) R (4) 4.52; they'll sell about 5 refrigerators if they run 4 ads per day. D) R (4) 203.36; they'll sell about 203 refrigerators if they run 4 ads per day. 4. Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + or – . x4 y = 10x + 1 ad when they're running 4 ads. B) R (4) 203.36; the cost of refrigerators will be rising by $203.36 if they're A) Does not exist x 2 x4 1 4 B) D) 9. An appliance store manager estimates that for x television ads run per day, R( x) 0.01x3 x 2 3x 200 refrigerators will be sold per month. Find R (4) and interpret what it tells us about sales. A) R (4) 4.52; sales will be increasing at about 5 refrigerators per month per 3. Find the indicated limit if it exists. lim y = 10x – 1 x 5 2x 1 decrease approximately by as x 7. How much will the function decreases from 3 to 2.7? A) 0.006 B) 0.06 C) 0.6 2. Determine the domain of the given function. C) B) –1 C) None f ( x) if 15 16 x 3 3x 15 8 x3 3x 72 x5 72 x5 1 3x 3 7 x2 C) D) f ( x) 5 3 72 x5 72 x 3x 3 3 f ( x) 3 3 8 x 3x x 11. The cost of producing x units of a certain commodity is C ( x) 3x2 5 x 5 dollars. If the price is p(x) = (41 – x) dollars per unit, determine the level of production that maximizes profit. A) x = 3 B) x = 1 C) x = 5 D) x = 2 D) 0 and –1 2 5 6. An equation for the tangent line to the curve y (7 x x 1) at the point where x = 1 3 2 12. Find the absolute minimum of the function f ( x) x 3x on the interval 1 x 5. A) 5 –4 B) –1 C) D) 0 f x xe36 x ; 2 3 2 13. Determine where the graph of f ( x) x 6 x 8x 4 A) For x > 2 For x < –2 B) C) For x > –2 is concave down. D) For x < 2 14. Determine the critical points of the given function and classify each critical point as a relative maximum, a relative minimum, or neither. f ( x) 3 x 4 8 x 3 6 x 2 3 A) B) (0, 2) neither; (1, 3) relative minimum (0, 2) relative minimum; (1, 3) relative maximum C) D) (0, 3) relative minimum; (1, 4) neither (0, 2) relative minimum; (1, 4) neither 15. Locate all inflection points of f ( x) x 4 6 x3 24 x 2 26 . A) (1, 9) and (–4, –486) B) (1, 9) C) None D) (0, 26) 16. Solve for x: a 7 x 1 b ln b 1 ln a C) 1 ln b x 1 1 7 ln a B) x D) ln b 7 ln a 2/9 dx C 2 1 y e36 x 2 3 1 36 x2 e 2 2 2 1 y 1 e36 x 2 D) A) u = x3 B) u x3 2x C) u 2x D) u ln x3 21. Water flows into a tank at the rate of 2t 5 ft3/min. If the tank is empty when t = 0, how much water does it contain 6 minutes later? Express the answer to two decimal places. A) 0.63 ft3 B) 19.64 ft3 C) 32.08 ft3 D) 24.74 ft3 x 1 32 + 5 x B) 2 2 5 C) 0, 2 5 D) 0, – 2 5 23. How quickly will $700 grow to $2,000 if interest is 8% compounded quarterly? Round your answer to two decimal places, if necessary. A) in 13.00 years B) in 13.15 years C) in 13.20 years D) in 13.25 years 3 24. Find the derivative of ln ln x 4 . 3 x ln x B) 12 x ln x C) 12 x ln x D) 12 ln(ln x) . 11/9 9 x 9 11 9 y C) ln x3 2 x dx A) C) 81 x 9 11 9 D) x2 9x C 18 11/9 B) 1 1 36 x 2 e 2 2 20. Specify the substitution you would choose to evaluate the integrals. A) 0 11/9 C y 1 9 per minute. How far does the object travel from the end of minute 2 to the end of minute 3? A) 37 meters B) 78 meters C) 157 meters D) 77 meters x A) 9 9 B) 1 ln b 1 7 ln a 2 17. An object is moving so that its velocity after t minutes is v(t ) 1 8t 9t meters x 9 9 18. Evaluate A) (–6, 1) 22. Find all real numbers x that satisfy the given equation. 7 A) 19. The slope f (x) at each point (x, y) on a curve y = f (x) is given, along with a particular point (a, b) on the curve. Use this information to find f (x). C 25. The graph of x 3e 3 has A) a relative maximum at x = 0 B) a relative minimum at x = 0 C) D) a point of inflection at x = 0 nothing significant at x = 0 國立嘉義大學 102 學年度基礎學科學力競賽試題卷: 科目: 經濟數學 題型:選擇題(共 25 題) 配分:100% 18. C 1. D 19. C 2. C 20. D 3. A 21. B 4. B 22. D 5. D 23. D 6. B 24. 7. A 25. C 8. C 9. A 10. B 11. C 12. B 13. D 14. C 15. A 16. B 17. B 3 A