L'Hospital's rule 1 more time?

0 ⤊

lim (1-x+ln(x))/(1+cos(pi x))
x->1

I come up with -1/2pi But I think I am wrong

2007-10-20 10:25:35 · 2 answers · asked by Smokey. 6 in Science & Mathematics ➔ Mathematics

I feel like such a dumb a** pi*pi is pi^2
not 2pi

2007-10-20 10:30:29 · update #1

limit = (-1 + 1/x) / (-π sinπx)
= (-1/x^2) / (-π^2 cosπx)
= -1 / π^2

2007-10-20 10:29:23 · answer #1 · answered by Dr D 7 · 0⤊ 0⤋

= lim (-1+1/x)/ (-pi sin pi x) = lim (1-x)/(-pi sin pix) = lim1/pi^2cospix = -1/pi^2

2007-10-20 10:33:02 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋