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Determine whether the function is continuous and differentiable at x = 2. If a y-value is undefined or a limit does not exist, type DNE. f(x) = x < 2 x² +3 x ≥2 (3x²-5

Determine whether the function is continuous and differentiable at x = 2. If a y-value is undefined or a limit does not exist, type DNE. f(x) = x < 2 x² +3 x ≥2 (3x²-5

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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Determine whether the function is continuous and differentiable at x = 2. If a y-value is undefined or a limit does not exist, type DNE. f(x) - (3x²_5_x 2 x²+3 x ≥ 2 ƒ(2) = lim f(x) = x→2 ƒ(2) Is f(x) continuous at x = 2? (Yes x-2- ƒ'(x) = lim_ƒ'(x) = lim x→2 lim_ƒ'(x) = x→2+ II Is f(x) differentiable at x = 2? (No due to a cusp x < 2 x > 2
Transcribed Image Text:Determine whether the function is continuous and differentiable at x = 2. If a y-value is undefined or a limit does not exist, type DNE. f(x) - (3x²_5_x 2 x²+3 x ≥ 2 ƒ(2) = lim f(x) = x→2 ƒ(2) Is f(x) continuous at x = 2? (Yes x-2- ƒ'(x) = lim_ƒ'(x) = lim x→2 lim_ƒ'(x) = x→2+ II Is f(x) differentiable at x = 2? (No due to a cusp x < 2 x > 2
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