Chapter 1: Q. 56 (page 98)

For each limit in Exercises 55鈥�64, use graphs and algebra to approximate the largest delta or smallest-magnitude N that corresponds to the given value of epsilon or M, according to the appropriate formal limit definition.
$\underset{x 鈫� 1^{+}}{l i m} \frac{1}{x^{2} - 1} = 鈭�, M = 10000, find largest 未 > 0$

Short Answer

Expert verified

The required value of $未鈮� 0.00005$

Step by step solution

Step 1. Given Information

The given function is $f (x) = \frac{1}{x^{2} - 1}$

Step 2. Explanation

From the given function, we have, $c = 1, M = 10000$

The limit expression can be written as a formal statement as below,

For allM positive, there exists a delta positive such that if $x 鈭� (1, 1 + 未)$

Then $\frac{1}{x^{2} - 1} 鈭� (10000, 鈭�)$

Now the largest value of delta is given by,

$\frac{1}{x^{2} - 1} = 10000 x^{2} - 1 = \frac{1}{10000} x^{2} = 0.0001 + 1 x = \sqrt{1.0001}$

Hence,

$未 = \sqrt{1.0001} - 1 鈮� 1.0000499 - 1 鈮� 0.0000499 鈮� 0.00005$

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91影视

For each limit in Exercises 55鈥�64, use graphs and algebra to approximate the largest delta or smallest-magnitude N that corresponds to the given value of epsilon or M, according to the appropriate formal limit definition.limx鈫�1+1x2-1=鈭�,M=10000,findlargest未>0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Applied Mathematics

Decision Maths

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.