Problem 1E: Find the limits in Exercises 1–12.
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Problem 2E: Find the limits in Exercises 1–12.
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Problem 3E: Find the limits in Exercises 1–12.
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Problem 4E: Find the limits in Exercises 1–12.
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Problem 5E: Find the limits in Exercises 1–12.
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Problem 6E: Find the limits in Exercises 1–12.
6.
Problem 7E: Find the limits in Exercises 1–12.
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Problem 8E Problem 9E: Find the limits in Exercises 1–12.
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Problem 10E Problem 11E: Find the limits in Exercises 1–12.
11.
Problem 12E Problem 13E: Find the limits in Exercises 13–24 by rewriting the fractions first.
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Problem 14E: Find the limits in Exercises 13–24 by rewriting the fractions first.
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Problem 15E: Find the limits in Exercises 13–24 by rewriting the fractions first.
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Problem 16E: Find the limits in Exercises 13–24 by rewriting the fractions first.
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Problem 17E: Find the limits in Exercises 13–24 by rewriting the fractions first.
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Problem 18E Problem 19E: Find the limits in Exercises 13–24 by rewriting the fractions first.
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Problem 20E Problem 21E: Find the limits in Exercises 13–24 by rewriting the fractions first.
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Problem 22E: Find the limits in Exercises 13–24 by rewriting the fractions first.
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Problem 23E: Find the limits in Exercises 13–24 by rewriting the fractions first.
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Problem 24E: Find the limits in Exercises 13–24 by rewriting the fractions first.
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Problem 25E: Find the limits in Exercises 25–30.
25.
Problem 26E Problem 27E Problem 28E Problem 29E Problem 30E Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E Problem 38E Problem 39E: At what points (x, y, z) in space are the functions in Exercises 35–40 continuous?
39.
h(x, y, z) =... Problem 40E Problem 41E: By considering different paths of approach, show that the functions in Exercises 4148 have no limit... Problem 42E: By considering different paths of approach, show that the functions in Exercises 41–48 have no limit... Problem 43E: By considering different paths of approach, show that the functions in Exercises 41–48 have no limit... Problem 44E Problem 45E: By considering different paths of approach, show that the functions in Exercises 41–48 have no limit... Problem 46E: By considering different paths of approach, show that the functions in Exercises 41–48 have no limit... Problem 47E: By considering different paths of approach, show that the functions in Exercises 41–48 have no limit... Problem 48E Problem 49E: In Exercises 49–54, show that the limits do not exist.
49.
Problem 50E: In Exercises 49–54, show that the limits do not exist.
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Problem 51E Problem 52E Problem 53E: In Exercises 49–54, show that the limits do not exist.
53.
Problem 54E Problem 55E: Let
Find each of the following limits, or explain that the limit does not exist.
Problem 56E: Let .
Find the following limits.
Problem 57E: Show that the function in Example 6 has limit 0 along every straight line approaching (0,... Problem 58E Problem 59E: The Sandwich Theorem for functions of two variables states that if g(x, y) ≤ f(x, y) ≤ h(x, y) for... Problem 60E: The Sandwich Theorem for functions of two variables states that if g(x, y) ≤ f(x, y) ≤ h(x, y) for... Problem 61E: The Sandwich Theorem for functions of two variables states that if g(x, y) ≤ f(x, y) ≤ h(x, y) for... Problem 62E: The Sandwich Theorem for functions of two variables states that if g(x, y) ≤ f(x, y) ≤ h(x, y) for... Problem 63E Problem 64E Problem 65E: In Exercises 65–70, find the limit of f as (x, y) → (0, 0) or show that the limit does not... Problem 66E: In Exercises 65–70, find the limit of f as (x, y) → (0, 0) or show that the limit does not... Problem 67E: In Exercises 65–70, find the limit of f as (x, y) → (0, 0) or show that the limit does not... Problem 68E Problem 69E Problem 70E: In Exercises 65–70, find the limit of f as (x, y) → (0, 0) or show that the limit does not... Problem 71E: In Exercises 71 and 72, define f(0, 0) in a way that extends f to be continuous at the origin.
71.... Problem 72E: In Exercises 71 and 72, define f(0, 0) in a way that extends f to be continuous at the origin.
72.... Problem 73E: Each of Exercises 73–78 gives a function f(x, y) and a positive number . In each exercise, show that... Problem 74E: Each of Exercises 73–78 gives a function f(x, y) and a positive number . In each exercise, show that... Problem 75E: Each of Exercises 73–78 gives a function f(x, y) and a positive number . In each exercise, show that... Problem 76E: Each of Exercises 73–78 gives a function f(x, y) and a positive number . In each exercise, show that... Problem 77E: Each of Exercises 73–78 gives a function f(x, y) and a positive number . In each exercise, show that... Problem 78E Problem 79E: Each of Exercises 79–82 gives a function f(x, y, z) and a positive number . In each exercise, show... Problem 80E Problem 81E: Each of Exercises 79–82 gives a function f(x, y, z) and a positive number . In each exercise, show... Problem 82E Problem 83E Problem 84E format_list_bulleted