Refer to image below. Let f(x) = 7³, and let z → 8, and suppose that & .001.Determine & so that if |1 − a| < 8, then |ƒ(1) – L\ < ɛ .|z

Answered: Let f(x) = ï³, and let z → 8, and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Refer to image below.

Let f(x) = 7³, and let z → 8, and suppose that & .001.
Determine & so that if |1 − a| < 8, then |ƒ(1) – L\ < ɛ .
|z

Expert Solution

Step 1

What is Limit of a Function:

The concept of a function's limit, which describes how a function behaves when it is near a specific input, is crucial to calculus and analysis in mathematics. A function's limit is the value it approaches when its parameter approaches a.a at a particular point in its domain. The core idea behind calculus and analysis is the notion of a limit. It is used to define the derivative and the definite integral and can also be used to examine how functions behave locally close to interesting locations.

Given:

Given function is $f (x) = x^{\frac{2}{3}}$ . It is given that $x \to 8$ and suppose $ε = 0.001$ .