Now consider f(x) = ! defined for all real numbers except for x = 0. Appealing to the e-8 definition, prove that no real number LER can be a limit of f(x) as x tends to 0, i.e., no matter what you choose for L, limz0 L. (3.1.4) Preliminary Work Wuit

Now consider f(x) = ! defined for all real numbers except for x = 0. Appealing to the e-8 definition, prove that no real number LER can be a limit of f(x) as x tends to 0, i.e., no matter what you choose for L, limz0 L. (3.1.4) Preliminary Work Wuit

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 52E

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Now consider f(x) = ! defined for all real numbers except for x = 0. Appealing to the e-8
definition, prove that no real number L e R can be a limit of f(x) as x tends to 0, i.e., no
matter what you choose for L, limg0÷7 L.
(3.1.4) Preliminary Work. Write your thought path here.
(3.1.5)
Formal Proof.

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