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Let f(x)=5x-3. Use the definition of limit of a function at a point to prove that the limit of this function as x approaches 3 is 12.

Let f(x)=5x-3. Use the definition of limit of a function at a point to prove that the limit of this function as x approaches 3 is 12.

Advanced Engineering Mathematics
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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4.1

Please include a formal proof.

Definition 3.2.1. Let I CR be an open interval, let c E I, let f: I - {c} → R be a function and let LER. The number L is the limit of f as x goes to c, written lim f(x) = L, %3D if for each ɛ > 0, there is some 8 > 0 such that x E I – {c} and |x – c| < d imply |f(x) – L| < ɛ. If lim f(x) = L, we also say that f converges to L as x goes to c. If f converges to some real number as x goes to c, we say that lim f(x) exists.
Transcribed Image Text:Definition 3.2.1. Let I CR be an open interval, let c E I, let f: I - {c} → R be a function and let LER. The number L is the limit of f as x goes to c, written lim f(x) = L, %3D if for each ɛ > 0, there is some 8 > 0 such that x E I – {c} and |x – c| < d imply |f(x) – L| < ɛ. If lim f(x) = L, we also say that f converges to L as x goes to c. If f converges to some real number as x goes to c, we say that lim f(x) exists.
Let f(x)=5x-3. Use the definition of limit of a function at a point to prove that the limit of this function as x approaches 3 is 12.
Transcribed Image Text:Let f(x)=5x-3. Use the definition of limit of a function at a point to prove that the limit of this function as x approaches 3 is 12.
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