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5 votes
Find the limit.

\lim_(x \to \infty) 5tan^(-1) (ln3x)

User Employee
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1 Answer

1 vote

\tan^(-1)x is continuous over its domain, so


\displaystyle\lim_(x\to\infty)5\tan^(-1)(\ln3x)=5\tan^(-1)\left(\lim_(x\to\infty)\ln3x\right)

and since
\ln3x\to\infty and
\tan^(-1)x\to\frac\pi2 as
x\to\infty, the value of the limit here would be
\frac{5\pi}2
User Thomas Rollet
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