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Let f be the function defined by f(x) = -3x² +1 x - 13 x < 2 x ≥ 2 (a) Evaluate lim f(x), lim f(x), and lim f(x). x-2- x 2+ x-2 (b) Is f continuous at 2? Use the definition of continuity to justify your answer. (c) If f differentiable at 2? Show the work that leads to your conclusion.

Let f be the function defined by f(x) = -3x² +1 x - 13 x < 2 x ≥ 2 (a) Evaluate lim f(x), lim f(x), and lim f(x). x-2- x 2+ x-2 (b) Is f continuous at 2? Use the definition of continuity to justify your answer. (c) If f differentiable at 2? Show the work that leads to your conclusion.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let f be the function defined by (a) Evaluate lim f(x), x-2- f(x): = -3x² +1 X - 13 " x < 2 x ≥ 2 lim f(x), and lim ƒ(x). x→2+ x→2 (b) Is f continuous at 2? Use the definition of continuity to justify your answer. (c) If f differentiable at 2? Show the work that leads to your conclusion.
Transcribed Image Text:Let f be the function defined by (a) Evaluate lim f(x), x-2- f(x): = -3x² +1 X - 13 " x < 2 x ≥ 2 lim f(x), and lim ƒ(x). x→2+ x→2 (b) Is f continuous at 2? Use the definition of continuity to justify your answer. (c) If f differentiable at 2? Show the work that leads to your conclusion.
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