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This question concerns the following exercise. Exercise Prove that the limit e sin(3x) 20 giả –sinh a lim 22 exists, and determine its value. (a) Explain why the following solution to this exercise is incorrect and/or incomplete identifying at least three errors or significant omissions in

This question concerns the following exercise. Exercise Prove that the limit e sin(3x) 20 giả –sinh a lim 22 exists, and determine its value. (a) Explain why the following solution to this exercise is incorrect and/or incomplete identifying at least three errors or significant omissions in

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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This question concerns the following exercise. Exercise Prove that the limit e sin(3x) lim 2-0 giả +sinh exists, and determine its value. (a) Explain why the following solution to this exercise is incorrect and/or incomplete, identifying at least three errors or significant omissions in the argument. For each error or omission, explain the mistake that the writer of the solution has made. (There may be more than three errors or omissions, but you need identify only three. These should not include incorrect statements or omissions that follow logically from earlier errors or omissions.) Solution (incorrect and/or incomplete!) Let f(x)=e* sin (3x) and g(x)=x²+ sinh *, * € R. Then f(0) 0 and g(0) = 0. So we can use l'Hôpital's Rule. Also, f'(x) e sin(3x)+3e cos(3r) and g'(x)=2x+coshx, ZER. Hence the limit e sin(3x) lim 2+0x2 +sinhư exists and equals "sin(3x)+ 3e cos(3r) lim 2x+cosha Substituting - 0 in the numerator and denominator, we get that this limit, and so the original limit, equals 0+3 3. 0+1 (b) Write out a correct solution to the exercise.
Transcribed Image Text:This question concerns the following exercise. Exercise Prove that the limit e sin(3x) lim 2-0 giả +sinh exists, and determine its value. (a) Explain why the following solution to this exercise is incorrect and/or incomplete, identifying at least three errors or significant omissions in the argument. For each error or omission, explain the mistake that the writer of the solution has made. (There may be more than three errors or omissions, but you need identify only three. These should not include incorrect statements or omissions that follow logically from earlier errors or omissions.) Solution (incorrect and/or incomplete!) Let f(x)=e* sin (3x) and g(x)=x²+ sinh *, * € R. Then f(0) 0 and g(0) = 0. So we can use l'Hôpital's Rule. Also, f'(x) e sin(3x)+3e cos(3r) and g'(x)=2x+coshx, ZER. Hence the limit e sin(3x) lim 2+0x2 +sinhư exists and equals "sin(3x)+ 3e cos(3r) lim 2x+cosha Substituting - 0 in the numerator and denominator, we get that this limit, and so the original limit, equals 0+3 3. 0+1 (b) Write out a correct solution to the exercise.
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