Question

Lim ln(tan x) as tends to pi/2 from the left

Answer 1

Let
`x=\arctan y`. Then
`\tan x=y`, and so as
`x\to\frac\pi2^-`, you have
`y\to+\infty`. The limit is then equivalent to


`\displaystyle\lim_(x\to\frac\pi2^-)\ln(\tan x)=\lim_(y\to\infty)\ln y=\infty`