Question

How do you find the limit of `x tan (8/x)` as x approaches infinity?

Answer 1

`8`.

Explanation:

Let `1/x=theta," so that, as "xrarroo, theta rarr0`.

Also, we know that, `lim_(thetararr0) tantheta/theta=1`.

`:." The Reqd. Limit="lim_(theta rarr 0) (tan8theta)/theta`

`=lim_(theta rarr 0) (tan8theta)/(8theta)(8)`

`=lim_(8thetararr0) (tan8theta)/(8theta)(8)`

`=(1)(8)=8`