Definition 3.2.1. Let /CR be an open interval, let c € 1, let f: 1- {c} → R be a function and let L E R. The number L is the limit of f as x goes to c, written lim f(x) = L., if for each ɛ > 0, there is some 8 > 0 such that x €I- {c} and |x – e| < 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. A Definition 3.3.1. Let ACR be a set, and let f:A→R be a function. 1. Let cE A. The function f is continuous at c if for each ɛ > 0, there is some 8 > O such that x E A and ļx– c| < 8 imply |f(x) –f(c) < ɛ. The function f is discontinuous at c if f is not continuous at c, in that case we also say that f has a discontinuity at c. 2. The function f is continuous if it is continuous at every number in A. The function f is discontinuous if it is not continuous.

Definition 3.2.1. Let /CR be an open interval, let c € 1, let f: 1- {c} → R be a function and let L E R. The number L is the limit of f as x goes to c, written lim f(x) = L., if for each ɛ > 0, there is some 8 > 0 such that x €I- {c} and |x – e| < 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. A Definition 3.3.1. Let ACR be a set, and let f:A→R be a function. 1. Let cE A. The function f is continuous at c if for each ɛ > 0, there is some 8 > O such that x E A and ļx– c| < 8 imply |f(x) –f(c) < ɛ. The function f is discontinuous at c if f is not continuous at c, in that case we also say that f has a discontinuity at c. 2. The function f is continuous if it is continuous at every number in A. The function f is discontinuous if it is not continuous.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.1: Inverse Functions

Problem 18E

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