Express-sinh-1-x-ln-x-in-terms-of-natural-logarithms-Hence-find-the-limit-as-x-

Question Number 178412 by Spillover last updated on 16/Oct/22

Express \sinh^{- 1} x - \ln x in terms of

natural logarithms . Hence find

the limit as x \to \infty

Answered by Ar Brandon last updated on 16/Oct/22

\sinh^{- 1} x - \ln x = \ln (x + \sqrt{1 + x^{2}}) - \ln x

\lim_{x \to \infty} = \underset{x \to \infty}{\lim l n} (\frac{x + \sqrt{1 + x^{2}}}{x})

= \underset{x \to \infty}{\lim l n} (1 + \sqrt{\frac{1}{x^{2}} + 1}) = \ln 2

Commented by Spillover last updated on 16/Oct/22

t h a n k s