Use the formulas given below to express tanh-1( - ) 6 logarithms. sinh - lu= In (ut Vư +1), uis any real number tanh 1 1 + u tanh 2 In ₁-₁ u<1 1-u csch-¹ u = In 1 u ¹ (-1)=( 6 + √1+u² |u| 2 cosh -¹ u = ln (u + √√²-1), uz 1 sech ¹u = In in terms of natural , u 0 coth¹u=- 1+√√1-u² u 1 u + 1 In 2 u-1' 2 |u|>1 0

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Use the formulas given below to express tanh
logarithms.
sinh -1u = In (ut Vư +1), uis
any real number
1
1+u
tanh u= In , |u| < 1
ū₁
1-u
2
csch -1,
¹u=
tanh
u = In
-|-
¹(-1)
6
=
1
√√₁+U²
2
lul
1
¹ (-1)
6
cosh¯¹u = ln (u+√√u² − 1), uz
2
sech ¹u = In
- 1u
u #0 coth
in terms of natural
1+√1-u²
u
1
In
2 u-1'
u + 1
, |u| > 1
0<u≤'
Transcribed Image Text:Use the formulas given below to express tanh logarithms. sinh -1u = In (ut Vư +1), uis any real number 1 1+u tanh u= In , |u| < 1 ū₁ 1-u 2 csch -1, ¹u= tanh u = In -|- ¹(-1) 6 = 1 √√₁+U² 2 lul 1 ¹ (-1) 6 cosh¯¹u = ln (u+√√u² − 1), uz 2 sech ¹u = In - 1u u #0 coth in terms of natural 1+√1-u² u 1 In 2 u-1' u + 1 , |u| > 1 0<u≤'
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