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

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

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

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

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

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

lim_(x rarr0)(e^(3x)-1)/(log(1+5x))

lim_(x rarr0)(e^(x)-1)/(log(1+x))

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

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