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(a) Show that helpful). (b) Evaluate lim x-0 coth x dx = log sinh x| + c. (Hint: you may find the substitution u = sinhx to be sinhæ X using l'Hôpital's Rule or otherwise. Check your result using a calculator. 1 ₁ (coth x - 1) (c) By treating as an improper integral, show that dx = = log (sinh 1).

(a) Show that helpful). (b) Evaluate lim x-0 coth x dx = log sinh x| + c. (Hint: you may find the substitution u = sinhx to be sinhæ X using l'Hôpital's Rule or otherwise. Check your result using a calculator. 1 ₁ (coth x - 1) (c) By treating as an improper integral, show that dx = = log (sinh 1).

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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(a) Show that I co coth x dx = log sinh x| + c. (Hint: you may find the substitution u = sinh x to be helpful). (b) Evaluate lim x →0 sinhæ X using l'Hôpital's Rule or otherwise. Check your result using a calculator. 1 L ( dæ = log (sinh 1). (c) By treating as an improper integral, show that coth x 1 X
Transcribed Image Text:(a) Show that I co coth x dx = log sinh x| + c. (Hint: you may find the substitution u = sinh x to be helpful). (b) Evaluate lim x →0 sinhæ X using l'Hôpital's Rule or otherwise. Check your result using a calculator. 1 L ( dæ = log (sinh 1). (c) By treating as an improper integral, show that coth x 1 X
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