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

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

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

lim_(xto0+)(x^n lnx),ngt0

|{:(x,e^(x-1),(x-1)^(3)),(x-lnx,cos(x-1),(x-1)^(2)),(tanx,sin^(2)x,cos^(2)x):}|=a_(0)+a_(1)(x-1)+a_(2)(x-1)^(2)cdots The value of cos^(-1) (a_(1)) is:

|{:(x,e^(x-1),(x-1)^(3)),(x-lnx,cos(x-1),(x-1)^(2)),(tanx,sin^(2)x,cos^(2)x):}|=a_(0)+a_(1)(x-1)+a_(2)(x-1)^(2)cdots The value of cos^(-1) (a_(1)) is:

If |{:(x,e^(x-1),(x-1)^(3)),(x-lnx,cos(x-1),(x-1)^(2)),(tanx,sin^(2)x,cos^(2)x):}|=a_(0)+a_(1)(x-1)+a_(2)(x-1)^(2)cdots The value of cos^(-1) (a_(1)) is

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

lim_(x rarr 1) ln(1-lnx)/(lnx^2)=

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

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