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.
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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.
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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.
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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.
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Problem 50E: In Exercises 49–54, show that the limits do not exist.
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Problem 51E: Let
Find each of the following limits, or explain that the limit does not exist.
Problem 52E: Let .
Find the following limits.
Problem 53E: Show that the function in Example 6 has limit 0 along every straight line approaching (0,... Problem 54E Problem 55E: The Sandwich Theorem for functions of two variables states that if g(x, y) ≤ f(x, y) ≤ h(x, y) for... Problem 56E: The Sandwich Theorem for functions of two variables states that if g(x, y) ≤ f(x, y) ≤ h(x, y) for... Problem 57E: The Sandwich Theorem for functions of two variables states that if g(x, y) ≤ f(x, y) ≤ h(x, y) for... Problem 58E: The Sandwich Theorem for functions of two variables states that if g(x, y) ≤ f(x, y) ≤ h(x, y) for... Problem 59E Problem 60E Problem 61E: In Exercises 65–70, find the limit of f as (x, y) → (0, 0) or show that the limit does not... Problem 62E: In Exercises 65–70, find the limit of f as (x, y) → (0, 0) or show that the limit does not... Problem 63E: In Exercises 65–70, find the limit of f as (x, y) → (0, 0) or show that the limit does not... Problem 64E Problem 65E 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 71 and 72, define f(0, 0) in a way that extends f to be continuous at the origin.
71.... Problem 68E: In Exercises 71 and 72, define f(0, 0) in a way that extends f to be continuous at the origin.
72.... Problem 69E: Each of Exercises 73–78 gives a function f(x, y) and a positive number . In each exercise, show that... Problem 70E: Each of Exercises 73–78 gives a function f(x, y) and a positive number . In each exercise, show that... Problem 71E: Each of Exercises 73–78 gives a function f(x, y) and a positive number . In each exercise, show that... Problem 72E: Each of Exercises 73–78 gives a function f(x, y) and a positive number . In each exercise, show that... Problem 73E: Each of Exercises 73–78 gives a function f(x, y) and a positive number . In each exercise, show that... Problem 74E Problem 75E: Each of Exercises 79–82 gives a function f(x, y, z) and a positive number . In each exercise, show... Problem 76E Problem 77E: Each of Exercises 79–82 gives a function f(x, y, z) and a positive number . In each exercise, show... Problem 78E Problem 79E Problem 80E format_list_bulleted