lim_(x rarr1)((1)/(ln x)-(1)/(x-1))

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 rarr1)((x)/(x-1)-(1)/(log x))

lim_(x rarr0)[(1)/(x)-(1)/(x^(2))log(1+x)]

lim_(x rarr1)(1)/(|1-x|)=

lim_(x rarr1)((x+5)(x-1))/(x-1)

lim_(x rarr1)(log x)/(x-1)=

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

lim_(x rarr0)(cot)^((1)/(log x))

If lim_(x rarr0)(a^(sin x)-1)/(1+x-cos x)=lim_(x rarr1)(x-1)/(ln(x)) then a=

8. Prove that lim_(x rarr1^(+))((1)/(x-1))!=lim_(x rarr1^(-))((1)/(x-1))