Answered: Using the definition of the limit, and…

Using the definition of the limit, and given that lim 00, r any N >0, there is a ô > 0 so that the following implication involving inequalities hold true:

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.4: Values Of The Trigonometric Functions

Problem 21E

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Question

For Calc.

0 <x -
< 8 implies that
<- N
Using the inequalities above, find the largest ô > 0 which satisfies the implication when N = 2022.
(ROUND TO FIVE DECIMAL PLACES WHEN NECESSARY.)

3. Using the definition of the limit, and given that
-7
lim
1-2* x - 2
o,
for any N > 0, there is a d > 0 so that the following implication involving inequalities hold true:

Expert Solution

Step 1

Given limit is $\lim_{x \to 2^{+}} \frac{- 7}{x - 2} = - \infty$ .

We know that for a function $f (x)$ , we have $\lim_{x \to a^{+}} f (x) = - \infty$ if for any arbitrary positive real number $N > 0$ , there exists a positive real number $δ > 0$ such that: