Test # 4 Review Math MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Test # 4 Review Math 25 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the integral. ) 4(2x + 5) A) 4 (2x + 5) 4 + C B) 4 (2x + 5) 4 + C C) 2 (2x + 5) 4 + C D) 8 (2x + 5) 4 + C ) 2) dr 6r - 7 2) A) 2 6r C B) 4 6r C C) 6r C D) 6 6r C ) y dy A) 9 5 ln 2 + 5y + C B) 8 5 ln 2 + 5y + C C) 9 ln 2 + 5y + C D) 8 ln 2 + 5y + C ) 4) ex ex + e 4) A) ln ex + e + C B) x + C C) e ln ex + e + C D) x e + C 5) (2 + ln x)x 5) A) ln 2 + ln x + C B) ln (2 + ln x) + C C) 2 ln 2 + ln x + C D) 2 ln 2 + ln x + C 6) The rate of expenditure of a particular machine is given by Mʹ(x) = 5x x2 + 5, where x is time measured in years. Maintenance costs through the second year are $ 4. Find the total maintenance function. A) M(x) = 5(x2 + 5) / B) M(x) = 5(x2 + 5) /2-2 C) M(x) = 5(x2 + 5) / D) M(x) = 5(x2 + 5) /2-2 6) Approximate the area under the curve and above the x -axis using n rectangles. Let the height of each rectangle be given by the value of the function at the right side of the rectangle. 7) f(x) = 2x2 + x + from x = 0 to x = 6; n = 6 7) A) 22 B) 2 C) 200 D) 20

2 Use the numeric integration feature on your calculator to find the integral. 8) (x4+ 2x- 2x2- x - ) - A) B).0667 C) -0.9 D) 6.9 8) The given marginal function has x measured in years and MR(x) in hundreds of dollars per year. Use numerical integration on a graphing calculator to find the total revenue over the given period. 9) MR(x) = 0.0x - 0.5x2 + 2x (0 x ) 9) A) $ B) -$, C) $7.72 D) $8.97 Evaluate the integral. 4 0) x/2 A) 4.67 B).4 C) 2.8 D) ) Evaluate the definite integral. x ) 0 5x2 + A) B).5647 C).565 D).565 ) 2) 6x + 9 x A) 9 ln - B) ln C) ln D) ln 2) Use the definite integral to find the area between the x -axis and the graph of f(x) over the indicated interval. ) f(x) = ex - ; [-2, ] A) 7.7 B) 5.0 C) 7.7 D) 7.2 ) 4) f(x) = ; [, 4] x 4) A) 4 B) 4 C) 2 D) 2 Find the area of the shaded region. 5) 5) A) 7.5 B) 2.5 C) 5 D) 0 2

3 6) 6) A) 2 B) 26 C) 22 D) 25 7) 7) A) 5 B) 5 C) D) 2 8) A certain company has found that its expenditure rate per day (in hundreds of dollars) on a certain type of job is given by Eʹ(x) = 6x + 7, where x is the number of days since the start of the job. Find the expenditure if the job takes 2 days. A) $2600 B) $9 C) $900 D) $26 8) 9) A certain object moves in such a way that its velocity (in m/s) after time t (in s) is given by v = t2 + 5t + 7. Find the distance traveled during the first four seconds. A) 68.0 m B) 89. m C) 4.0 m D) 6. m 9) Find the area bounded by the given curves. 20) y = 2x - x2, y = 2x - 4 A) 2 B) 7 C) D) 4 20) Use a graphing calculator to approximate the area between the graphs of the pair of functions on the given interval. 2) y = x and y = + x - x 2; [, 5] 2) A) 4.69 B) C) 2.07 D) ) Find the producerʹs surplus if the supply function of some item is given by S(x) = x2 + 2x + 8. Assume that supply and demand are in equilibrium at x = 0. A) 8,900 B) 9,800 C) 2,700 D) 7,200 22)

4 Use a table of integrals to solve the problem. 2) The rate of growth of a microbe population is given by mʹ(x) = 0xe2x, where x is time in days. What is the change in population in the first days? A) 60,544 B) 5,6 C) 0,272 D) 5,29 2) Find the general solution of the differential equation. 24) dy = 8x 2 A) 6x + C B) x + C C) x + C D) 8x + C 24) Find the particular solution of the differential equation. 25) dy = 4x + 4; y = - when x = 0 A) y = 4x2 + 4x B) y = 4x2 + 4x - C) y = 2x2 + 4x - D) y = 2x2 + 4x ) 26) Assume that the rate of change of the population of a certain city is given by dy dt = 6000e.06t, where y is the population at time t, in years. The population was 00,000 in 980. Assume t = 0 is 980. Find the population function. A) y = 00,000e.06t B) y = 0,000e.06t + 90,000 C) y = 00,000e.06 D) y =,000,000e ,000 26) Evaluate the function. 27) Find f(-7, 2) when f(x, y) = 5x + 2y - 7. A) -4 B) -8 C) - D) ) 28) The number of cows that can graze on a ranch is approximated by C(x,y) = 9x + 5y - 2, where x is the number of acres of grass and y the number of acres of alfalfa. If the ranch has 55 acres of alfalfa and 0 acres of grass, how many cows may graze? A) 64 cows B) 545 cows C) 645 cows D) 54 cows 28) Find the partial derivative. 29) Let z = f(x,y) = 9x2 - xy + 8y. Find z x. A) -x - 24y B) -x + 24y2 C) 8x - y D) 8x + y2 29) Find the partial derivative as requested. 0) fy if f(x,y) = x + 2x2y2-6y2 A) 4yx - 4y B) + 4yx2 C) 4yx2-2y D) 4yx - 2y 0) ) fx(9, -5) if f(x,y) = 7x2-9xy A) -8 B) 7 C) 8 D) 62 ) 4

5 2) fy(5, -6) if f(x,y) = 7x2-9xy A) -45 B) 29 C) -54 D) 9 2) Find the second-order partial derivative. ) Find fxx when f(x,y) = 8xy - 7y2 + 2x. A) -4 B) -28 C) 24x2 D) 48xy ) 5

6 Answer Key Testname: TEST # 4 REVIEW MATH 25 ) C 2) C ) A 4) A 5) A 6) D 7) A 8) D 9) A 0) A ) C 2) D ) B 4) C 5) D 6) B 7) D 8) A 9) B 20) A 2) B 22) A 2) B 24) A 25) C 26) A 27) B 28) D 29) C 0) C ) B 2) A ) D 6