L'Hospital's rule to find limits

[MathewsMD]

Homework Statement

Find the limit, using L'Hospital's rule, if appropriate.
lim lnxtan(pix/2)
x->1^+

Homework Equations

The Attempt at a Solution

http://imgur.com/gbhQutU

I've done this question and gotten the correct answer by making lnx the numerator and 1/tan(pix/2) the denominator, but get the wrong answer when I make tan(pix/2) the numerator and 1/lnx the denominator. Is this because you cannot have -infinity/infinity? My solution is posted, and any help on where I went wrong or what steps to take would be very helpful.

 

[iRaid]

Disregard.

 

[Dick]

Homework Statement

Find the limit, using L'Hospital's rule, if appropriate.
lim lnxtan(pix/2)
x->1^+

Homework Equations

The Attempt at a Solution

http://imgur.com/gbhQutU

I've done this question and gotten the correct answer by making lnx the numerator and 1/tan(pix/2) the denominator, but get the wrong answer when I make tan(pix/2) the numerator and 1/lnx the denominator. Is this because you cannot have -infinity/infinity? My solution is posted, and any help on where I went wrong or what steps to take would be very helpful.

You didn't do anything wrong in the second attempt, but sometimes one way of arranging the ratio for l'Hospital's gives you an easy solution and another way doesn't lead anywhere. The second attempt is just giving you more infinity/infinity type limits. You aren't getting a wrong answer, you just aren't getting any answer that's not still indeterminant. That's why it's worth thinking about alternatives before you start.