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Graph the function defined by (1 {} g(r) = + cos(πr/2) for -2≤r≤2 for r< -2 or r> 2.

Graph the function defined by (1 {} g(r) = + cos(πr/2) for -2≤r≤2 for r< -2 or r> 2.

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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Graph the function defined by -{- g(r) = 1 + cos(πr/2) for for -2 ≤r≤2 r< -2 or r > 2. (a) Is g continuous at r = 2? Explain your answer. O Yes, the graph of g is continuous, because the value of g at r = 2 is equal to the value as you approach from the left and from the right. O No, the graph of g is not continuous, because the value of g at r = 2 is not equal to the value as you approach from the left. O No, the graph of g is not continuous, because the value of g at r = 2 is not equal to the value as you approach from the right. No, the graph of g is not continuous, because the value of g at r = 2 is not equal to the value as you approach from the left or the right. O No, the graph of g is not continuous, because g does not exist at r = 2. (b) Do you think g is differentiable at r = 2? Explain your answer. O Yes, g is differentiable, because the graph does not have a corner at r = 2 and the slope at that point is 0. O No, g is not differentiable, because the graph has a corner at r = 2. O No, g is not differentiable, because the graph does not have a corner at r = 2. O No, g is not differentiable, because the slope at r = 2 is 0. O No, g is not differentiable, because the slope at r = 2 is not 0.
Transcribed Image Text:Graph the function defined by -{- g(r) = 1 + cos(πr/2) for for -2 ≤r≤2 r< -2 or r > 2. (a) Is g continuous at r = 2? Explain your answer. O Yes, the graph of g is continuous, because the value of g at r = 2 is equal to the value as you approach from the left and from the right. O No, the graph of g is not continuous, because the value of g at r = 2 is not equal to the value as you approach from the left. O No, the graph of g is not continuous, because the value of g at r = 2 is not equal to the value as you approach from the right. No, the graph of g is not continuous, because the value of g at r = 2 is not equal to the value as you approach from the left or the right. O No, the graph of g is not continuous, because g does not exist at r = 2. (b) Do you think g is differentiable at r = 2? Explain your answer. O Yes, g is differentiable, because the graph does not have a corner at r = 2 and the slope at that point is 0. O No, g is not differentiable, because the graph has a corner at r = 2. O No, g is not differentiable, because the graph does not have a corner at r = 2. O No, g is not differentiable, because the slope at r = 2 is 0. O No, g is not differentiable, because the slope at r = 2 is not 0.
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