Question

how to use l'Hospital's rule effectively in conjunction with other laws and techniques, such as in lim*infinity (x^2+x)^(1/2)-x or lim*infinity (x-lnx) or lim*infinity ((1/lnx)-(1/(x-1)))

Answer 1

L'Hospital's ONLY APPLY when you have \[\frac{ 0 }{ 0 } or \frac{ \infty }{ \infty } \]

Answer 2

Can you lease explain how \[\lim_{x \rightarrow infinity} ((1/lnx)-(1/(x-1))) = infinity\]

Answer 3

\[\lim_{x \rightarrow infinity} (x^2logx-xlog^2x)/(xlogx)\] has been presented as an intermediate step, but how was it determined to multiply both numerator and denominator by \[xlogx\]?

Answer 4

*so as to comply with the \[\infty/\] condition