Problem 1RE: Find formulas for the functions described in Exercises 18. A line with slope 2 and x-intercept 5. Problem 2RE: Find formulas for the functions described in Exercises 18. A parabola opening downward with its... Problem 3RE: Find formulas for the functions described in Exercises 18. A parabola with x-intercepts 1 and... Problem 4RE: Find formulas for the functions described in Exercises 18. The bottom half of a circle centered at... Problem 5RE: Find formulas for the functions described in Exercises 18. The top half of a circle with center (1,... Problem 6RE: Find formulas for the functions described in Exercises 18. A cubic polynomial having x-intercepts at... Problem 7RE: Find formulas for the functions described in Exercises 18. A rational function of the form y = ax/(x... Problem 8RE: Find formulas for the functions described in Exercises 18. A cosine curve with a maximum at (0, 5),... Problem 9RE: Find derivatives for the functions in Exercises 1-73. Assume a, b, c, and k are constants. 9.... Problem 10RE: If g(x) = (4 x2)/(x2 + x), find the domain of g(x). Solve g(x) = 0. Problem 11RE: The entire graph of f(x) is shown in Figure 1.1. a) What is the domain of f(x)? b) What is the range... Problem 12RE: For f(n) = 3n2 2 and g(n) = n +1, find and simplify: a) f(n) + g(n) b) f(n)g(n) c) The domain of... Problem 13RE: Let m = f(A) be the minimum annual gross income, in thousands of dollars, needed to obtain a 30-year... Problem 14RE: For Exercises 1417, solve for t using logs. 5t = 7 Problem 15RE: For Exercises 1417, solve for t using logs. 2 = (1.02)t Problem 16RE: For Exercises 1417, solve for t using logs. 7 3t = 5 2t Problem 17RE: For Exercises 1417, solve for t using logs. 5.02(1.04)t = 12.01(1.03)t Problem 18RE: In Exercises 1819, put the functions in the form P = P0ekt. P = P02t Problem 19RE: In Exercises 1819, put the functions in the form P = P0ekt. P = 5.23(0.2)t Problem 20RE: For Exercises 2021, find functions f and g such that h(x) = f(g(x)). [Note: Do not choose f(x) = x... Problem 21RE: For Exercises 2021, find functions f and g such that h(x) = f(g(x)). [Note: Do not choose f(x) = x... Problem 22RE: Find the amplitudes and periods in Exercises 2223. y = 5 sin (x/3) Problem 23RE: Find the amplitudes and periods in Exercises 2223. y = 4 2 cos(5x) Problem 24RE: Consider the function y = 5 + cos(3x). (a) What is its amplitude? (b) What is its period? (c) Sketch... Problem 25RE: Determine the end behavior of each function as x + and as x . (a) f(x)=x7 (b) f(x)=3x+7x312x4 (c)... Problem 26RE: In Exercises 2627, which function dominates as x ? 102xor72,000x12 Problem 27RE: In Exercises 2627, which function dominates as x ? 0.25xor25,000x3 Problem 28RE: Find possible formulas for the graphs in Exercises 2841. Problem 29RE: Find possible formulas for the graphs in Exercises 2841. Problem 30RE: Find possible formulas for the graphs in Exercises 2841. Problem 31RE: Find possible formulas for the graphs in Exercises 2841. Problem 32RE: Find possible formulas for the graphs in Exercises 2841. Problem 33RE: Find possible formulas for the graphs in Exercises 2841. Problem 34RE: Find possible formulas for the graphs in Exercises 2841. Problem 35RE: Find possible formulas for the graphs in Exercises 2841. Problem 36RE: Find possible formulas for the graphs in Exercises 2841. Problem 37RE: Find possible formulas for the graphs in Exercises 2841. Problem 38RE: Find possible formulas for the graphs in Exercises 2841. Problem 39RE: Find possible formulas for the graphs in Exercises 2841. Problem 40RE: Find possible formulas for the graphs in Exercises 2841. Problem 41RE: Find possible formulas for the graphs in Exercises 2841. Problem 42RE: Are the functions in Exercises 4243 continuous on [1, 1]? g(x)=1x2+1 Problem 43RE: Are the functions in Exercises 4243 continuous on [1, 1]? h(x)=11x2 Problem 44RE: Use Figure 1.2 to estimate the limits if they exist: (a) limx0f(x) (b) (b) limx1f(x) (c) limx2f(x)... Problem 45RE: For the functions in Exercises 4546, use algebra to evaluate the limits limxa+f(x), limxaf(x), and... Problem 46RE: For the functions in Exercises 4546, use algebra to evaluate the limits limxa+f(x), limxaf(x), and... Problem 47RE: Use the graph of g(t) in Figure 1.3 to give approximate values for the following limits (if they... Problem 48RE: Use Figure 1.4 to give approximate values for the following limits (if they exist). (a) limx2f(x)... Problem 49RE: In Exercises 4952, is the function continuous on the interval? xx2+2 on [2, 2] Problem 50RE: In Exercises 4952, is the function continuous on the interval? 2x+x2/3 on [1, 1] Problem 51RE: In Exercises 4952, is the function continuous on the interval? 1sinx on [2,2] Problem 52RE: In Exercises 4952, is the function continuous on the interval? exex1 on [1, 1] Problem 53RE: Use a graph to estimate each of the limits in Exercises 5356. Use radians unless degrees are... Problem 54RE: Use a graph to estimate each of the limits in Exercises 5356. Use radians unless degrees are... Problem 55RE: Use a graph to estimate each of the limits in Exercises 5356. Use radians unless degrees are... Problem 56RE: Use a graph to estimate each of the limits in Exercises 5356. Use radians unless degrees are... Problem 57RE: In Exercises 5758, (a) Make a table of values of f(x) for x = 0.9, 0.99, 1.01, and 1.1. (b) Use the... Problem 58RE: In Exercises 5758, (a) Make a table of values of f(x) for x = 0.9, 0.99, 1.01, and 1.1. (b) Use the... Problem 59RE: For Exercises 5961, use the end behavior of the denominator and numerator to find the limit as x .... Problem 60RE: For Exercises 5961, use the end behavior of the denominator and numerator to find the limit as x .... Problem 61RE: For Exercises 5961, use the end behavior of the denominator and numerator to find the limit as x .... Problem 62RE: For Exercises 6263, create a function, f(x), such that limx1f(x)=5 Problem 63RE: For Exercises 6263, create a function, f(x), such that limxf(x)=12. Problem 64RE: Evaluate the limits of the following function, or explain why they do not exist.... Problem 65RE: Evaluate the limits of the following function, or explain why they do not exist.... Problem 66RE: Evaluate the limits of the following function, or explain why they do not exist.... Problem 67RE: In Exercises 6772, use algebra to find the limit exactly. limx5x225x5 Problem 68RE: In Exercises 6772, use algebra to find the limit exactly. limx4x4x216 Problem 69RE: In Exercises 6772, use algebra to find the limit exactly. limx2x25x+6x2 Problem 70RE: In Exercises 6772, use algebra to find the limit exactly. limx3x3x2+2x15 Problem 71RE: In Exercises 6772, use algebra to find the limit exactly. limx2x2+8x2x22 Problem 72RE: In Exercises 6772, use algebra to find the limit exactly. limh0(4+h)242h2 Problem 73RE: The yield, Y, of an apple orchard (in bushels) as a function of the amount, a, of fertilizer (in... Problem 74RE: The graph of Fahrenheit temperature, F, as a function of Celsius temperature, C, is a line. You know... Problem 75RE: The demand function for a certain product, q = D(p), is linear, where p is the price per item in... Problem 76RE: A flight from Dulles Airport in Washington, DC, to La-Guardia Airport in New York City has to circle... Problem 77RE: The force, F, between two atoms depends on the distance r separating them. See Figure 1.6. A... Problem 78RE: When the Olympic Games were held outside Mexico City in 1968, there was much discussion about the... Problem 79RE: The population of the Ukraine fell from 46.01 million in 2010 to 45.43 million in 2014.1 Assuming... Problem 80RE: During April 2006, Zimbabwes inflation rate averaged 0.67% a day. This means that, on average,... Problem 81RE Problem 82RE: A kilogram weighs about 2.2 pounds. (a) Write a formula for the function, f, which gives an objects... Problem 83RE: The graph of f(x) is a parabola that opens upward and the graph of g(x) is a line with negative... Problem 84RE: Each of the functions in the table is increasing over its domain, but each increases in a different... Problem 85RE: A culture of 100 bacteria doubles after 2 hours. How long will it take for the number of bacteria to... Problem 86RE: If f(x) = a ln(x + 2), how does increasing a affect (a) The y-intercept? (b) The x-intercept? Problem 87RE: What is the doubling time of prices which are increasing by 5% a year? Problem 88RE: Find the half-life of a radioactive substance that is reduced by 30% in 20 hours. Problem 89RE: The air in a factory is being filtered so that the quantity of a pollutant, P (in mg/liter), is... Problem 90RE: The half-life of radioactive strontium-90 is 29 years. In 1960, radioactive strontium-90 was... Problem 91RE: What is the period of the motion of the minute hand of a clock? Problem 92RE: In an electrical outlet, the voltage, V, in volts, is given as a function of time, t, in seconds, by... Problem 93RE: In a US household, the voltage in volts in an electric outlet is given by V=156sin(120t), where t is... Problem 94RE: (a) How does the parameter A affect the graph of y = A sin(Bx)? (Plot for A = 1, 2, 3 with B = 1.)... Problem 95RE: Water is flowing down a cylindrical pipe of radius r. (a) Write a formula for the volume, V, of... Problem 96RE: Values of three functions are given in Table 1.1, rounded to two decimal places. Two are power... Problem 97RE: Figure 1.8 shows the hat function hN(x)={0ifxN11+xNifN1xN1+NxifNxN+10ifN+1x. (a) Graph the function... Problem 98RE: The point P moves around the circle of radius 5 shown in Figure 1.9. The angle , in radians, is... Problem 99RE: Match the following functions with the graphs in Figure 1.11. Assume 0 b a. (a) y=axx (b)... Problem 100RE: Use a computer or calculator to sketch the functions y(x) = sin x and zk(x) = kx for k =... Problem 101RE: If possible, choose k so that the following function is continuous on any interval:... Problem 102RE: Find k so that the following function is continuous on any interval: j(x)={kcosxx0exkx0 Problem 103RE: A car is coasting down a hill at a constant speed. A truck collides with the rear of the car,... Problem 104RE: By graphing y = 3 2et estimate the limit limt(32et). Use the properties of limits and the fact that... Problem 105RE: Evaluate the limits of the following function, or explain why they do not exist.... Problem 106RE: (a) For k = 1, sketch f(x)={kx0x2(x2)2+32x4. (b) Find the value of k so that f(x) is continuous at x... Problem 107RE: (a) Graph a continuous function g with all the following properties: (i) g(2) = 5 (ii) g(x) has a... Problem 108RE: In Problems 108111, let g(t) be a function whose graph has a vertical asymptote at t = 5 and... Problem 109RE: In Problems 108111, let g(t) be a function whose graph has a vertical asymptote at t = 5 and... Problem 110RE: In Problems 108111, let g(t) be a function whose graph has a vertical asymptote at t = 5 and... Problem 111RE: In Problems 108111, let g(t) be a function whose graph has a vertical asymptote at t = 5 and... Problem 112RE: In Problems 112113, use the given value of f(5) and the values of f(x) in the table. (a) Assuming it... Problem 113RE: In Problems 112113, use the given value of f(5) and the values of f(x) in the table. (a) Assuming it... Problem 114RE: In Problems 114116, find the limits. limh01/(x+h)21/x2h Problem 115RE: In Problems 114116, find the limits. limh0x+hxh Problem 116RE: In Problems 114116, find the limits. limh02(x+h)3(x+h)2(2x3x2)h Problem 117RE: For Problems 117120, if possible, calculate the limits using the properties of limits. Justify each... Problem 118RE: For Problems 117120, if possible, calculate the limits using the properties of limits. Justify each... Problem 119RE: For Problems 117120, if possible, calculate the limits using the properties of limits. Justify each... Problem 120RE: For problems 117-120, if possible, calculate the limits using the properties of limits. Justify each... Problem 121RE: For Problems 121124, evaluate the limit, using the rules for limits together with limxax=a and... Problem 122RE: For Problems 121124, evaluate the limit, using the rules for limits together with limxax=a and... Problem 123RE: For Problems 121124, evaluate the limit, using the rules for limits together with limxax=a and... Problem 124RE: For Problems 121124, evaluate the limit, using the rules for limits together with limxax=a and... Problem 125RE: The notation limx0+ means that we only consider values of x greater than 0. Estimate the limit... Problem 126RE: Let limxf(x)= and limxg(x)=. Give possible formulas for f(x) and g(x) if (a) limxf(x)+g(x)= (b)... Problem 127RE: (a) Evaluate the limit limx0(x1x). (b) Explain why you cannot use Property 3 of the limit properties... Problem 128RE: For the functions in Problems 128135, do the following: (a) Make a table of values of f(x) for x =... Problem 129RE: For the functions in Problems 128135, do the following: (a) Make a table of values of f(x) for x =... Problem 130RE: For the functions in Problems 128135, do the following: (a) Make a table of values of f(x) for x =... Problem 131RE: For the functions in Problems 128135, do the following: (a) Make a table of values of f(x) for x =... Problem 132RE: For the functions in Problems 128135, do the following: (a) Make a table of values of f(x) for x =... Problem 133RE: For the functions in Problems 128135, do the following: (a) Make a table of values of f(x) for x =... Problem 134RE: For the functions in Problems 128135, do the following: (a) Make a table of values of f(x) for x =... Problem 135RE: For the functions in Problems 128135, do the following: (a) Make a table of values of f(x) for x =... format_list_bulleted
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