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Numerade Educator

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Problem 25 Medium Difficulty

Give an alternative solution to Example 3 by letting $ y = \sinh^{-1} x $ and then using Exercise 9 and Example 1(a) with $ x $ replaced by $ y. $

Answer

$y=\ln (x+\sqrt{1+x^{2}})$

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Video Transcript

We know that if we let why equals sign age to the negative One other words the inverse Then we know that sign Each of why is Max Therefore we have co sign HR wy as plus on my ass square root of one plus x squared. Therefore we have either Why modest acts is poster minus were of one plus x squared. Therefore, we have the natural log of each of the wise. We're taking the natural for both sides. This gives us sign H to the negative one of acts People's the not true along of exposed the square root of one plus X squared.