`L_(x->1)(1/(lnx)-1/(x-1))=`

lim_(x->e) (lnx-1)/(x-e)

Using the L .Hospital rule find limits of the following functions : lim_(x to 1)(1/(ln x)-x/(lnx))

Find the following limits: lim_(xrarr1)(1/(x-1)-1/(lnx))

lim_(x->1)(x^2-x*lnx+lnx-1)/(x-1)

Using the L .Hospital rule find limits of the following functions : lim_(xto1) (a^(lnx)-x)/(lnx)

Find the following limits: lim_(xrarr1) (lnx)/(x^2-1)

Evaluate: ("Lim")_(x->1)(x^x-x)/(x-1-lnx)

The value of Lim_(x->oo)(xln(1+lnx/x))/lnx

Read the following passages and answer the following questions (7-9) Consider the integrals of the form l=inte^(x)(f(x)+f'(x))dx By product rule considering e^(x)f(x) as first integral and e^(x)f'(x) as second one, we get l=e^(x)f(x)-int(f(x)+f'(x))dx=e^(x)f(x)+c int((1)/(lnx)-(1)/((lnx)^(2)))dx is equal to