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4. For the0:04:03

4. For the function g whose graph is given, state the following. (a) lim(x→∞)⁡g(x) (b) lim(x→-∞)⁡g(x

3. For the0:02:16

3. For the function f whose graph is given, state the following. (a) lim(x→∞)⁡f(x) (b) lim(x→-∞)⁡

2. (a) Can0:03:32

2. (a) Can the graph of y=f(x) intersect a vertical asymptote? Can it intersect a horizontal asympt

1. Explain in0:01:46

1. Explain in your own words the meaning of each of the following. (a) lim(x→∞)⁡f(x)=5

73. A Tibetan0:05:07

73. A Tibetan monk leaves the monastery at 7:00 AM and takes his usual path to the top of the mount

72. (a) Show0:06:59

72. (a) Show that the absolute value function F(x)=|x| is continuous everywhere.

71. Show that0:05:14

71. Show that the function f(x)=(x^4 sin⁡(1/x)if x≠0, 0 if x=0} is continuous on (-∞,∞).

Can You Count0:01:00

Can You Count To A Googol?

64. To prove0:03:40

64. To prove that sine is continuous, we need to show that lim(x→a)⁡sin⁡(a+h) =sin⁡a for every real

63. Prove that0:04:13

63. Prove that f is continuous at a if and only if (lim)(h→0)f(a+h)=f(a)

62. Prove, without0:04:47

62. Prove, without graphing, that the graph of the function has at least two x-intercepts in the

60. (a) Prove0:04:01

60. (a) Prove that the equation has at least one real root. (b) Use your graphing device to find the

Can You Make0:01:00

Can You Make A Rational Number From Irrationals?

59. (a) Prove0:04:12

59. (a) Prove that the equation has at least one real root. (b) Use your graphing device to find the

58. (a) Prove0:05:22

58. (a) Prove that the equation has at least one real root. (b) Use your calculator to find an

57. (a) Prove0:05:46

57. (a) Prove that the equation has at least one real root. (b) Use your calculator to find an

56. Use the0:02:52

56. Use the Intermediate Value Theorem to show that there is a root of the given equation in the

55. Use the0:02:20

55. Use the Intermediate Value Theorem to show that there is a root of the given equation in the

54. Use the0:03:45

54. Use the Intermediate Value Theorem to show that there is a root of the given equation in the

53. Use the0:01:58

53. Use the Intermediate Value Theorem to show that there is a root of the given equation in the

50. Suppose that0:04:04

50. Suppose that a function f is continuous on [0,1] except at 0.25 and that f(0)=1 and f(1)=3.

49. Which of0:05:54

49. Which of the following functions f has a removable discontinuity at a? If the discontinuity

48. Let f(x)=1/x0:03:21

48. Let f(x)=1/x and g(x)=1/x^2. (a) Find (f∘g)(x). (b) Is f∘g continuous everywhere? Explain.

47. Suppose f0:02:45

47. Suppose f and g are continuous functions such that g(2)=6 and (lim)(x→2)[3f(x)+f(x)g(x)]=36.