Limit (cos(1\x))|tan x| x-> .5pi

[rambo123]

Homework Statement

having a hard time figuring out. I know the answer if infinite but having a hard time proving it

Homework Equations

tan x = cot (.5pi - x) did not help

The Attempt at a Solution

tried substituting t = 1\x got stuck

thanks

 

[HallsofIvy]

The limit as x goes to what?

 

[rambo123]

x goes to (pi)(1\2)

pi 3.14...

 

[Bohrok]

lim_x→π/2cos(1/x) exists, so what's left is lim_x→π/2|tan x|, which is infinite.