L ' Hospital Rule

lim x-> 0+ (xln|tanx|)
=lim x-> 0+ (ln (tanx))/(1/x)
=lim x-> 0+ (1/tanx)(secx)^2/(1/x^2)
=lim x-> 0+ (x^2sinx)/(cosx)^3
= 0
Similar for lim x-> 0- (xln|tanx|)
So lim x-> 0 (xln|tanx|) = 0




2009-08-09 13:12:31 補充：
=lim x-> 0+ (1/tanx)(secx)^2/(1/x^2) missing the minus sign but the answer is still 0