T Diagnostic Tests 1 Functions And Limits 2 Derivatives 3 Inverse Functions: Exponential, Logarithmic, And Inverse Trigonometric Functions 4 Applications Of Differentiation 5 Integrals 6 Techniques Of Integration 7 Applications Of Integration 8 Series 9 Parametric Equations And Polar Coordinates 10 Vectors And The Geometry Of Space 11 Partial Derivatives 12 Multiple Integrals 13 Vector Calculus A Trigonometry B Sigma Notation C The Logarithm Defined As An Integral expand_more
1.1 Functions And Their Representation 1.2 A Catalog Of Essential Functions 1.3 The Limit Of A Function 1.4 Calculating Limits 1.5 Continuity 1.6 Limits Involving Infinity Chapter Questions expand_more
Problem 1E: Write an equation that expresses the fact that a function f is continuous at the number 4. Problem 2E: If f is continuous on ( , ).what can you say about its graph? Problem 3E: (a) From the graph of f , state the numbers at which f is discontinuous and explain why. (b) For... Problem 4E: From the graph of g, state the intervals on which g is continuous. Problem 5E: Sketch the graph of a function f that is continuous except for the stated discontinuity.... Problem 6E: Sketch the graph of a function f that is continuous except for the stated discontinuity.... Problem 7E: Sketch the graph of a function f that is continuous except for the stated discontinuity. Removable... Problem 8E: Sketch the graph of a function f that is continuous except for the stated discontinuity. Neither... Problem 9E: The toll T charged for driving on a certain stretch of a toll road is 5 except during rush hours... Problem 10E: Explain why each function is continuous or discontinuous. (a) The temperature at a specific location... Problem 13E: Use the definition of continuity and the properties of limits to show that the function is... Problem 12E: Use the definition of continuity and the properties of limits to show that the function is... Problem 14E: Use the definition of continuity and the properties of limits to show that the function f(x)=x16x2... Problem 15E: Explain why the function is discontinuous at the given number a. Sketch the graph of the function.... Problem 16E: Explain why the function is discontinuous at the given number a. Sketch the graph of the function.... Problem 17E: Explain why the function is discontinuous at the given number a. Sketch the graph of the function.... Problem 18E: Explain why the function is discontinuous at the given number a. Sketch the graph of the function.... Problem 19E: Explain, using Theorems 4, 5, 6, and 8, why the function is continuous at every number in its... Problem 20E: Explain, using Theorems 4, 5, 6, and 8, why the function is continuous at every number in its... Problem 21E: Explain, using Theorems 4, 5, 6, and 8, why the function is continuous at every number in its... Problem 22E: Explain, using Theorems 4, 5, 6, and 8, why the function is continuous at every number in its... Problem 23E: Explain, using Theorems 4, 5, 6, and 8, why the function is continuous at every number in its... Problem 24E: Explain, using Theorems 4, 5, 6, and 8, why the function is continuous at every number in its... Problem 25E: Locate the discontinuities of the function and illustrate by graphing. 25. y=11+sinx Problem 26E: Locate the discontinuities of the function and illustrate by graphing. y=tanx Problem 27E Problem 28E: Use continuity to evaluate the limit. limxsin(x+sinx) Problem 29E: Show that f is continuous on (, ). f(x)={x2ifx1xifx1 Problem 30E: Show that f is continuous on ( , ). f(x)={sinxifx/4cosxifx/4 Problem 31E: Find the numbers at which the function f(x)={x+2ifx02x2if0x12xifx1 is discontinuous. At which of... Problem 32E: The gravitational force exerted by the planet Earth on a unit mass at a distance r from the center... Problem 33E: For what value of the constant c is the function f continuous on ( , )? f(x)={cx2+2xifx2x3cxifx2 Problem 34E: Find the values of a and h that make f continuous everywhere. f(x)={x24x2ifx2ax2bx+3ifxx32xa+bifx2 Problem 11E: Suppose f and g are continuous functions such that g(2) = 6 and limx2[3f(x)+f(x)g(x)]=36. Find f(2). Problem 35E: Which of the following functions .f has a removable discontinuity at a? If the discontinuity is... Problem 36E: Suppose that a function f is continuous on [0, 1] except at 0.25 and that f(0) = 1 and f(l) = 3. Let... Problem 37E: If f(x) = x2 + 10 sin x, show that there is a number c such that f(c) = 1000. Problem 38E: Suppose f is continuous on [1, 5] and the only solutions of the equation f(x) = 6 arc x = 1 and x =... Problem 39E: Use the Intermediate Value Theorem to show that there is a root of the given equation in the... Problem 40E: Use the Intermediate Value Theorem to show that there is a root of the given equation in the... Problem 41E: Use the Intermediate Value Theorem to show that there is a root of the given equation in the... Problem 42E: Use the Intermediate Value Theorem to show that there is a root of the given equation in the... Problem 43E Problem 44E Problem 45E Problem 46E: (a) Prove that the equation has at least one real root. (b) Use your graphing device to find the... Problem 47E: Is there a number that is exactly 1 more than its cube? Problem 48E Problem 49E Problem 50E Problem 51E: A Tibetan monk leaves the monastery at 7:00 AM and takes his usual path to the top of the mountain,... format_list_bulleted