" 6."lim_(x rarr1)(log x)/(x-1)=

Lim_(x rarre)(log x-1)/(x-e)=

lim_(x rarr0)(log(1+x))/(x)=1

lim_(x rarr0)(sin log(1-x))/(x)

lim_(x rarr0)(log_(e)(1+x))/(x)

Prove quad that quad (i) lim_(x rarr0)(a^(x)-1)/(x)=log_(e)aquad (ii) lim_(x rarr0)(log_(1+x))/(x)=1

The value of lim_(x rarr1)(log x)/(sin pi x) is

let a=lim_(x rarr1)((x)/(ln x)-(1)/(x ln x)),b=lim_(x rarr0)((x^(3)-16x)/(4x+x^(2))),c=lim_(x rarr0)(ln(1+sin x))/(x) and d=lim_(x rarr-1)((x+1)^(3))/(3[sin(x+1)-(x+1)]) then the matrix [[a,bc,d]]

lim_(x rarr 0) (log(1+x))/(3^x-1)=1/(log_(e)(3))

L=lim_(x rarr oo)((log x)/(x))^((1)/(x))