Problem 1E: (a) Using Figure 1.108, find all values of x for which f is not continuous. (b) List the largest... Problem 2E: (a) Using Figure 1.109, find all values of x for which f is not continuous. (b) List the largest... Problem 3E: Use the graph of f(x) in Figure 1.110 to give approximate values for the following limits (if they... Problem 4E: In Exercises 45, the graph of y = f(x) is given. (a) Give the x-values where f(x) is not continuous.... Problem 5E: In Exercises 45, the graph of y = f(x) is given. (a) Give the x-values where f(x) is not continuous.... Problem 6E: Assume f(x) is continuous on an interval around x = 0, except possibly at x = 0. What does the table... Problem 7E: Assume g(t) is continuous on an interval around t = 3, except possibly at t = 3. What does the table... Problem 8E: In Exercises 89, (a) Make a table of values of f(x) for x = 0.1, 0.01, 0.01, and 0.1. (b) Use the... Problem 9E: In Exercises 89, (a) Make a table of values of f(x) for x = 0.1, 0.01, 0.01, and 0.1. (b) Use the... Problem 10E: Use a table of values to estimate limx1(5+lnx). Problem 11E: In Exercises 1116, is the function continuous on the interval? 1x2on[1,1] Problem 12E: In Exercises 1116, is the function continuous on the interval? 1x2on[0,3] Problem 13E: In Exercises 1116, is the function continuous on the interval? 12x5on[3,4] Problem 14E: In Exercises 1116, is the function continuous on the interval? 2x+x1on[1,1] Problem 15E: In Exercises 1116, is the function continuous on the interval? 1cosxon[0,] Problem 16E: In Exercises 1116, is the function continuous on the interval? esincoson[4,4] Problem 17E: Are the following functions continuous? Explain. (a)f(x)={xx1x21x(b)g(x)={xx3x23x Problem 18E: Let f be the function given by f(x)={4x0x3x28x+173x5122x5x6. (a) Find all values of x for which f is... Problem 19E: In Exercises 1922, show there is a number c, with 0 c 1, such that f(c) = 0. f(x)=x3+x21 Problem 20E: In Exercises 1922, show there is a number c, with 0 c 1, such that f(c) = 0. f(x)=ex3x Problem 21E: In Exercises 1922, show there is a number c, with 0 c 1, such that f(c) = 0. f(x)=xcosx Problem 22E: In Exercises 1922, show there is a number c, with 0 c 1, such that f(c) = 0. f(x)=2x1/x Problem 23E: In Exercises 2328, use algebra to find the limit exactly. limx2x24x2 Problem 24E: In Exercises 2328, use algebra to find the limit exactly. limx3x29x+3 Problem 25E: In Exercises 2328, use algebra to find the limit exactly. limx1x2+4x5x1 Problem 26E: In Exercises 2328, use algebra to find the limit exactly. limx1x24x+3x2+3x4 Problem 27E: In Exercises 2328, use algebra to find the limit exactly. limx1x2+4x+8 Problem 28E: In Exercises 2328, use algebra to find the limit exactly. limh0(5+h)252h Problem 29E: For Exercises 2930, find the value of the constant k such that limx5(kx+10)=20 Problem 30E: For Exercises 2930, find the value of the constant k such that limx2(x+6)(xk)x2+x=4 Problem 31E: In Exercises 3134 find k so that the function is continuous on any interval. f(x)={kxx353x Problem 32E: In Exercises 3134 find k so that the function is continuous on any interval. f(x)={kx0x252x Problem 33E: In Exercises 3134 find k so that the function is continuous on any interval. h(x)={kx0x1x+31x5 Problem 34E: In Exercises 3134 find k so that the function is continuous on any interval. g(t)={1+kt5kt5t Problem 35E: Which of the following are continuous functions of time? (a) The quantity of gas in the tank of a... Problem 36E: An electrical circuit switches instantaneously from a 6-volt battery to a 12-volt battery 7 seconds... Problem 37E: A stone dropped from the top of a cliff falls freely for 5 seconds before it hits the ground. Figure... Problem 38E: Beginning at time t = 0, a car undergoing a crash test accelerates for two seconds, maintains a... Problem 39E: Discuss the continuity of the function g graphed in Figure 1.114 and defined as follows:... Problem 40E: Is the following function continuous on [1, 1]? f(x)={x|x|x00x=0 Problem 41E: Estimate the limits in Problems 4142 graphically. limx0|x|x Problem 42E: Estimate the limits in Problems 4142 graphically. limx0xln|x| Problem 43E: In Problems 4348, use a graph to estimate the limit. Use radians unless degrees are indicated by .... Problem 44E: In Problems 4348, use a graph to estimate the limit. Use radians unless degrees are indicated by .... Problem 45E: In Problems 4348, use a graph to estimate the limit. Use radians unless degrees are indicated by .... Problem 46E: In Problems 4348, use a graph to estimate the limit. Use radians unless degrees are indicated by .... Problem 47E: In Problems 4348, use a graph to estimate the limit. Use radians unless degrees are indicated by .... Problem 48E: In Problems 4348, use a graph to estimate the limit. Use radians unless degrees are indicated by .... Problem 49E: In Problems 4954, find a value of k, if any, making (x) continuous on [0, 5]. h(x)={kcosx0x12xx Problem 50E: In Problems 4954, find a value of k, if any, making (x) continuous on [0, 5]. h(x)={kx0x12kx+31x5 Problem 51E: In Problems 4954, find a value of k, if any, making (x) continuous on [0, 5]. h(x)={ksinx0xx+4x5 Problem 52E: In Problems 4954, find a value of k, if any, making (x) continuous on [0, 5]. h(x)={ekx0x2x+12x5 Problem 53E: In Problems 4954, find a value of k, if any, making (x) continuous on [0, 5].... Problem 54E: In Problems 4954, find a value of k, if any, making (x) continuous on [0, 5].... Problem 55E: (a) Use Figure 1.115 to decide at what points f(x) is not continuous. (b) At what points is the... Problem 56E: For t in months, a population, in thousands, is approximated by a continuous function... Problem 57E: A 0.6ml dose of a drug is injected into a patient steadily for half a second. At the end of this... Problem 58E: In Problems 5861, at what values of x is the function not continuous? If possible, give a value for... Problem 59E: In Problems 5861, at what values of x is the function not continuous? If possible, give a value for... Problem 60E: In Problems 5861, at what values of x is the function not continuous? If possible, give a value for... Problem 61E: In Problems 5861, at what values of x is the function not continuous? If possible, give a value for... Problem 62E: In Problems 6265, is the function continuous for all x? If not, say where it is not continuous and... Problem 63E: In Problems 6265, is the function continuous for all x? If not, say where it is not continuous and... Problem 64E: In Problems 6265, is the function continuous for all x? If not, say where it is not continuous and... Problem 65E: In Problems 6265, is the function continuous for all x? If not, say where it is not continuous and... Problem 66E: Graph three different functions, continuous on 0 x 1, and with the values in the table. The first... Problem 67E: Let p(x) be a cubic polynomial with p(5) 0, p(10) 0, and p(12) 0. What can you say about the... Problem 68E: (a) What does a graph of y = ex and y = 4 x2 tell you about the solutions to the equation ex = 4 ... Problem 69E: (a) Does f(x) satisfy the conditions for the Intermediate Value Theorem on 0 x 2 if a.... Problem 70E: Let g(x) be continuous with g(0) = 3, g(1) = 8, g(2) = 4. Use the Intermediate Value Theorem to... Problem 71E: By graphing y = (1 + x)1x, estimate limx0(1+x)1/x. You should recognize the answer you get. What... Problem 72E: Investigate limh0(1+h)1/h numerically. Problem 73E: Let f(x) = sin(1x). (a) Find a sequence of x-values that approach 0 such that sin(1x) = 0. [Hint:... Problem 74E: In Problems 7476, explain what is wrong with the statement. For any function f(x), if f(a) = 2 and... Problem 75E: In Problems 7476, explain what is wrong with the statement. If f(x) is continuous on 0 x 2 and if... Problem 76E: In Problems 7476, explain what is wrong with the statement. if limxcf(x) exists, then f(x) is... Problem 77E: In Problems 7780, give an example of: A function which is defined for all x and continuous... Problem 78E: In Problems 7780, give an example of: A function to which the Intermediate Value Theorem does not... Problem 79E: In Problems 7780, give an example of: A function that is continuous on [0, 1] but not continuous on... Problem 80E: In Problems 7780, give an example of: A function that is increasing but not continuous on [0, 10]. Problem 81E: Are the statements in Problems 8183 true or false? Give an explanation for your answer. If a... Problem 82E: Are the statements in Problems 8183 true or false? Give an explanation for your answer. If f is... Problem 83E: Are the statements in Problems 8183 true or false? Give an explanation for your answer. If f(x) is... format_list_bulleted
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage