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Which of the following functions f has a removable discontinuity at a? If the discontinuity is removable, find a function g that agrees with f for x = a and is continuous at a. (If an answer does not exist, enter DNE.) (a) f(x) = ) = x² = 1₁ O The discontinuity is removable. O The discontinuity is not removable. g(x) = (b) f(x) = x³ = x² = 6x₁, - a = 3 x - 3 O The discontinuity is removable. O The discontinuity is not removable. g(x) = _(c) __f(x) = [sin x], a = 1 g(x) = a = π (Recall that O The discontinuity is removable. O The discontinuity is not removable. [h(x)] means the largest integer that is less than or equal to h(x).)

Which of the following functions f has a removable discontinuity at a? If the discontinuity is removable, find a function g that agrees with f for x = a and is continuous at a. (If an answer does not exist, enter DNE.) (a) f(x) = ) = x² = 1₁ O The discontinuity is removable. O The discontinuity is not removable. g(x) = (b) f(x) = x³ = x² = 6x₁, - a = 3 x - 3 O The discontinuity is removable. O The discontinuity is not removable. g(x) = _(c) __f(x) = [sin x], a = 1 g(x) = a = π (Recall that O The discontinuity is removable. O The discontinuity is not removable. [h(x)] means the largest integer that is less than or equal to h(x).)

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Which of the following functions f has a removable discontinuity at a? If the discontinuity is removable, find a function g that agrees with ffor x = a and is continuous at a. (If an answer does not exist, enter DNE.) (a) f(x)=x²-1 a = 1 x-1 O The discontinuity is removable. O The discontinuity is not removable. g(x) = x³ - x² - 6x x - 3 The discontinuity is removable. O The discontinuity is not removable. (b) f(x) = g(x) = a = 3 (c) f(x) = [sin x], a = π (Recall that O The discontinuity is removable. O The discontinuity is not removable. g(x) = [h(x)] means the largest integer that is less than or equal to h(x).)
Transcribed Image Text:Which of the following functions f has a removable discontinuity at a? If the discontinuity is removable, find a function g that agrees with ffor x = a and is continuous at a. (If an answer does not exist, enter DNE.) (a) f(x)=x²-1 a = 1 x-1 O The discontinuity is removable. O The discontinuity is not removable. g(x) = x³ - x² - 6x x - 3 The discontinuity is removable. O The discontinuity is not removable. (b) f(x) = g(x) = a = 3 (c) f(x) = [sin x], a = π (Recall that O The discontinuity is removable. O The discontinuity is not removable. g(x) = [h(x)] means the largest integer that is less than or equal to h(x).)
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