2. lim(11x + 4) = 4

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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INSTRUCTIONS: By the formal definition of limit, show that the following limits are correct.
2. lim(11x + 4) = 4
Transcribed Image Text:INSTRUCTIONS: By the formal definition of limit, show that the following limits are correct. 2. lim(11x + 4) = 4
1. lim (7x + 8) = 29
X-3
Solution:
Let e > 0.
(1) WTF: 8 > 0 such that if 0< |x- 31 < 8, then |(7x +8) - 29 <E.
|(7x + 8) – 29| - 17x +8– 29| <E
- 17x – 21| < €
- 7|x – 3| <€
- x- 3|<
Choose 8 =
(2) Given e > 0, choose & = Then, if 0 < |x - 3| < 8, it implies that
|(7x + 8) – 29||
= 17x + 8- 29|
= 17x – 21|
=D 기x-31 < 78
%3D 기x-31 < 7 ()
= 7|x – 3| <€
%3D
By the formal definition of limit, lim(7x + 8) = 29.
X-3
Transcribed Image Text:1. lim (7x + 8) = 29 X-3 Solution: Let e > 0. (1) WTF: 8 > 0 such that if 0< |x- 31 < 8, then |(7x +8) - 29 <E. |(7x + 8) – 29| - 17x +8– 29| <E - 17x – 21| < € - 7|x – 3| <€ - x- 3|< Choose 8 = (2) Given e > 0, choose & = Then, if 0 < |x - 3| < 8, it implies that |(7x + 8) – 29|| = 17x + 8- 29| = 17x – 21| =D 기x-31 < 78 %3D 기x-31 < 7 () = 7|x – 3| <€ %3D By the formal definition of limit, lim(7x + 8) = 29. X-3
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