41. Show that if u = tanh(x/2), then 2u 1+u? 1- u?' 2du 1- u? cosh x = sinh x = 1- u? dx = Hint: For the first relation, use the identities sinh? (5) = (cosh x – 1), cosh () = (cosh x + 1)
41. Show that if u = tanh(x/2), then 2u 1+u? 1- u?' 2du 1- u? cosh x = sinh x = 1- u? dx = Hint: For the first relation, use the identities sinh? (5) = (cosh x – 1), cosh () = (cosh x + 1)
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...
Related questions
Question
![41. Show that if u =
tanh(x/2), then
2u
1+u?
1- u?'
2du
1- u?
cosh x =
sinh x =
1- u?
dx =
Hint: For the first relation, use the identities
sinh? (5) = (cosh x – 1),
cosh () =
(cosh x + 1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac2c7a5b-8c1e-421a-b062-9f8b02f611cd%2F0a905809-ae74-4fa1-9480-48606630eb94%2F4r2uq7z.png&w=3840&q=75)
Transcribed Image Text:41. Show that if u =
tanh(x/2), then
2u
1+u?
1- u?'
2du
1- u?
cosh x =
sinh x =
1- u?
dx =
Hint: For the first relation, use the identities
sinh? (5) = (cosh x – 1),
cosh () =
(cosh x + 1)
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