Explanation Given information : lim x → 1 − f ( x ) = 3 and lim x → 1 + f ( x ) = 7 Calculation: The limit lim x → 1 − f ( x ) = 3 Means that for x < 1 the value of f ( x ) can be made as close to 3 as one demands but not necessarily equal provided x is sufficiently close to 1 The limit lim

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 2.3, Problem 2E

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To explain: meaning of limx→1−f(x)=3 and limx→1+f(x)=7 and limx→1f(x) exists.

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Chapter 2.3, Problem 1E

Chapter 2.3, Problem 3E

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Figure out that this statement is true or false? if is false explain why? by using example, and if it is true explain why? When lim x → a f ( x ) exists, the limit is always equal to f ( a ) - Is this statement true or false?

determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If lim x→7 g(x) = 0 and lim x→7 f(x)/g(x) = 0 exists, then lim x→7 f(x) = 0. True. If lim x→7 f(x) is not equal to zero and lim x→7 g(x) = 0, then lim x→7 f(x)/g(x) does not exist. True. Any number divided by zero is equal to zero. False. Let g(x) = (x − 7) and f(x) = (x − 1)(x − 7). Then lim x→7 g(x) = 0 and lim x→7 f(x)/g(x) = 0 exists, but lim x→7 f(x) is not equal to 0. False. Divison by zero is not allowed. False. There is not enough information given to determine lim x→7 f(x)/g(x)

Guess the value of lim x 0 (tanx-x)/x3

Chapter 2 Solutions

Biocalculus

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meaning of lim x → 1 − f ( x ) = 3 and lim x → 1 + f ( x ) = 7 and lim x → 1 f ( x ) exists.

Solution Summary: The author explains that the limit of undersetxto alimf(x-)=L does not exist.

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To explain: meaning of limx→1−f(x)=3 and limx→1+f(x)=7 and limx→1f(x) exists.

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Chapter 2 Solutions