CHMath

ctrapterffi ;:I::ry 1 Assignmentr||!|l Decide from the graph whether each limit exists. lf a limit exists, estimate its value. lim F(x) x--+2 lim F(x) x--+ 1 What is the value of the limit? Select the correct choice below and fill in any answer boxes in your choice. A. tim F(x) = x-->2 (Type an integer or a simplified fraction.) B. The limit does not exist. What is the value of the limit? Select the correct choice below and fill in any answer boxes in your choice. A. tim F(x) = x--+ 1 (Type an integer or a simplified fraction.) B. The limit does not exist. 2. Use the properties of limits to help decide whether the limit exists. lf the limit exists, find its value *2-10 lim - . x-4 x+4 Select the correct choice below and, if necessary, fill in the answer box within your choice. *2-16 lim = x-4 \-4 (Simplify your answer.) The limit does not exist and is neither oo nor - oo. 3. Use the properties of limits to help decide whether the limit exists. lf the limit exists, find its value. 5x ,9 ,,* Select the correct choice below and, if necessary, fill in the answer box within your choice. 5x ,1 nr* = (Simplify your answer. Type an integer or a fraction.) The limit does not exist and is neither oo nor - oo. A.

B.

A. I of 11 B. crrapterffi 3600t The system of the population of a culture of tumor cells is given by p(t) = t + 1 Select the correct choice below, and fill in the answer box if necessary. lim P(t) = t-+oo The limit does not exist. Choose the correct statement. ; : A. The number of tumor cells gets closer to 3600 as time increases. , -, B. The number of tumor cells gets closer to oo as time decreases. ., , C. The number of tumor cells gets closer to 3600 as time decreases. .' : D. The number of tumor cells gets closer to oo as time increases" 5. Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. *2 -49 f(x) = x_z Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (Use a comma to separate answers as needed.) l- , A. f is discontinuous at the two values x = and is not oo or - m. The limit for the larger value is ' - , B' f is discontinuous at the two values x = . The limit for the larger value is ,,. j -, C. f is discontinuous at the single value x = ..,. O. f is discontinuous at the two values x = not oo or - oo. -,, g. f is continuous for all values of x. .. p. f is discontinuous over the interval . The limit is (Type your answer in interval notatiJn.) ,, C. t is discontinuous at the two values x = . The limit for the smaller value is . The limit for the larger value does not exist and is not oo or * oo. 4. A.

B.

H. f is discontinuous over the interval (Type your answer in interval notation.) l. f is discontinuous at the single value x = Find and interpret lim p(t). t-> m . The limit for the smaller value does not exist . The limit for the smaller value is . The limit is . The limit for both values do not exist and are . The limit does not exist and is not m or - oo" . The limit does not exist and is not oo or - oo. 2of11 chapterllII 6. (a) Graph the given function, (b) find all values of x where the function is discontinuous, and (c) find the limit from the left and the right at any values of x where the function is discontinuous. ( -s irx<2 I f(x)={ x+1 il2=x<4 I Is if x>4 (a) Choose the correct graph below. (b) Select the correct choice below and, if necessary, fill in the answer box within your choice. ' -; A. The function is discontinuous at x = (Use a comma to separate answers "" n""O"O.j i -'l B. The function is continuous for all values of x. (c) Find the limit or limits from the left and from the right for any values of x found in part (b). Select the correct choice below and, if necessary, fill in the answer boxes within your choice. . -, A. The limit(s) from the left is/are The limit(s) ftom the right is/are (Use a comma to separate ans*eiJ i* neeoeo.l i-: B. No discontinuities were found in part (b). 3of11 iln Chapterf The cost to transport a mobile home depends on the distance, x, in miles that the home is moved. Let C(x) represent the cost to move a mobile home x miles. One firm charges as follows. (a) Find the cost to move a mobile home 149 miles. $ (b) Find the cost to move a mobile home 150 miles. $ (c) Find the cost to move a mobile home 231 miles. $ (d) Find the cost to move a mobile home 400 miles. $ (e) Find the cost to move a mobile home 624 miles. $ (f) Where is C discontinuous? C is discontinuous at x = (Use a comma to separate answers as needed.) Cost per Mile $4.25 $3.50 $3.00 Distance in Miles 0

8' Suppose that f(t) = t2 + 4t - 5. What is the average rate of change of f(t) The average rate of change of f(t) over the interval 5 to 6 is over the interval 5 to 6? 9' Suppose the position of an object moving in a straight line is given by s(t) = 3t2 + 5t + 2. Find the instantaneous velocitywhent=6.

The instantaneous velocity at t = 6 is 4 of ll 1 0 ' Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) = 2x2 - 7x + 8. Complete partsathroughdbelow.

a. Find the average rate of change of profit as x changes from 4 to 6. per item b. Find the average rate of change of profit as x changes from 4 to 5. per item c. Find and interpret the instantaneous rate of change of profit with respect to the number of items produced when x = 4. (This number is called the marginal profit at x = 4.) per item What does this result mean? Choose the correct answer below. ", A. U/hen items are sold for $ , the profit is decreasing at the rate of $4 per item. .; B. When 4 items are sold, the profit is decreasing at the rate of $ . per item. ., C. When 4 items are sold, the profit is increasing at the rate of $ per item. :.-.r rr. Wh€n 4 ltems afe SOIO, Ine prOflt lS lnCreaslng aI me fate OT S .... , per llem. :', D. When items are sold for $ , the profit is increasing at the rate of $4 per item. d. Find the marginal profit at x = 6. per item 11. The distance of a particle from some fixed point is given by the following function. s(t) =12 +1- 2 a. What is the average rate of change of s(t) over the interval 1 lo 2? The average rate of change over the interval 1 to 2 is b. What is the average rate of change of s(t) over the interval 1 to 3? The average rate of change over the interval 1 to 3 is c. \,Vhat is the instantaneous rate of change of s(t) when t = 1? The instantaneous rate of change when t = 1 is 5of11 II:n chaptert 12. Estimate the slope (slope = rise/run) of the tangent line to the curve. \A/hat is your estimate of the slope? slope = (Round to the nearest integer.) -1 01 2 3 4 5 6 7I I 13. Using the definition of the derivative, find f'(x). Then flnd f'(1), f'(2), and f'(3) when the derivative exists. f(x)= *x2 +5x-3 f'(r) = _ (Type an expression using x as the variable.) Select the correct answer below and, if necessary fill in the answer box to complete your choice. - A. f,(1)= (Type an integer or a simplified fraction.) i--": a. the derivative does not exist. Select the correct answer below and, if necessary fill in the answer box to complete your choice. , , A. f,(2)= (l-ype an integer or a simplified fraction.) i- i B. The derivative does not exist. Select the correct answer below and, if necessary fill in the answer box to complete your choice. , A. f,(3)= (Type an integer or a simplified fraction.) i_.i B. The derivative does not exist. 14. For the given function, find (a) the equation of the secant line through the points where x has the given values and (b) the equation of the tangent line when x has the first value. y=f(x) =*2 *r; x= -4, x= -2 The equation of the secant line is y = a.

b. 6of11 The equation of the tangent line is y = chapterlll 15. Suppose the demand for a certain item is given by D(p) = - 4p2 - 8p * SOO, where p represents the price of the item in dollars. a. Find the rate of change of demand with respect to price. b. Find and interpret the rate of change of demand when the price is $9. a. The rate of change of demand with respect to price is . (Simplify your answer.) b. Choose the correct answer below and fill in any answer boxes in your choice. . -'r A. When the price is $9, demand is decreasing at a rate of about in price of $1. i--'l B. When the price is $9, demand is decreasing at a rate of about in price of $9. i"-"i C' When the price is $9, demand is increasing at a rate of about in price of $9. r'- r D. When the price is $9, demand is increasing at a rate of about in price of $1. items for each increase items for each increase items for each increase items for each increase 7 ofll chapterlff! 16. 8ofll r;n Chapterfll, The graph shows the temperature one holiday of an oven. The oven was lit at 8:30 A.M. Let T(x) be the temperature x hours after 8:30 A.M. (a) Find and interpret T'(0.5). How can T'(0.5) be found? : . A. Find the slope of the line that includes the points (2. j B. Find the slope of the line that includes the points (0. ,.', C. Find the change in y-values and add to the change points (0.5,170) and (2.5,850). ,-: D. Find the slope of the line that includes the points (5, Find and interpret T'(0.5). Select the correct answer below and fill in the answer box to complete your answer. (Round to the nearest integer as needed.) 850" cleaning cycle 9:30 10:30 11:30 12:30 1:30 2:30 3:30 (b) Find and interpret T'(3). Select the correct answer below and fill in the answer box to complete your answer. (Round to the nearest integer as needed.) A. T'(0.5) = T'(0.5)" per hour. B. T',(0.5) = per hour. c. T'(0.5) = ; The oven temperature is ; The oven temperature is ; The oven temperature is ; The oven temperature is in ; The oven temperature is dr ; The oven temperature is nr A. T'(3) = hour. B. T'(3) = hour. c. T'(3) = (c) Find T'(6.75). (Round to the nearest integer as needed.) l- : A- 1'16.751 = ; The oven temperature i: lr'1o.zs1l" per hour. ,.', B. T,(6.75)= ; The oven temperature ir lr'1o.zsyl" per hour. c. T',(6.75) = (d) At a certain time, a turkey was put into the oven, causing the oven temperature to drop. Estimate when the turkey was put into the oven. At which point in the graph is the oven temperature going down? i.,. A. When the slope of the line starts decreasing. i' : B. When the slope of the line starts increasing. r r C. When the slope of the line is 0. Estimate when the turkey was put into the oven. 9ofll Chapterlf ,45 ' 15 30 r00 (1) (2) -. A.M. , , P.M. 17 . Sketch the graph of the derivative of the function shown. Choose the correct graph below 18. When the price of an essential commodity rises rapidly, consumption drops slowly at first. lf the price continues to rise, however, a "tipping" point may be reached, at which consumption takes a sudden substantial drop. Suppose the accompanying graph shows the consumption of gasoline, G(t), in millions of gallons, in a certain area. Assume that the price is rising rapidly. Here t is the time in months after the price began rising. Sketch a graph of the rate of change in consumption as a function of time. Choose the correct graph below. A.

A. 10of11 ctupt"rl|lll 19. The groMh remaining in sitting height, y, at consecutive skeletal age levels is indicated for boys in the graph to the right. Sketch a graph showing the rate of change of growth remaining for the indicated years. Use the graph and your sketch to estimate the remaining growth and the rate of change of remaining growth for a 1S-year-old boy. Determine how to graph the rate of change in the discharge with respect to time. The graph of the rate of change will be positive when the graph of the growth remaining is (1) The graph of the rate of change will be negative when the graph of the growth remaining is (2) Choose the graph that best represents the rate of change. Determine the remaining growth for a 1S-year-old boy. The remaining growth for a 1S-year-old boy is approximately (Round to the nearest integer as needed.) Determine the rate of change of the remaining growth for a 1S-year-old boy. The rate of change is approximately cm (3) per year. (Type an integer or decimal rounded to one decimal place as needed.) cm. (1) ' ., increasing. i.-.:. decreasing. (2) r.": increasing. i-.: decreasing. (3) i": less ,._.1 mOfe ll of 1l