Chapter 1: Q. 64 (page 98)

For each limit in Exercises 55–64, 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.
$\underset{x \to \infty}{l i m} (4 - x^{2}) = - \infty, M = - 10000, find smallest N > 0$

Short Answer

Expert verified

The required value of $N \approx 100.02$

Step by step solution

Step 1. Given Information

The given function is $f (x) = 4 - x^{2}$

Step 2. Explanation

From the given function, we have, $c = \infty, L = - \infty$

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

For allM negative, there is someN positive such that if $x \in (N, \infty)$

Then $f (x) \in (- \infty, M)$

Now the smallest value of N is given by,

$4 - x^{2} = - 10000 x^{2} = 10004 x = \sqrt{10004} x \approx 100.02$

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For each limit in Exercises 55–64, 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→∞(4-x2)=-∞,M=-10000,findsmallestN>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

Statistics

Discrete Mathematics

Mechanics Maths

Decision Maths

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.