Find the limit. \lim_(x \to \infty) 5tan^(-1) (ln3x)

Question

Find the limit.

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

Answer 1

`\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`