Evaluate `lim_(l rarr1)(l^(m)-1)/(l^(n)-1)`

L_(x rarr1)((1)/(ln x)-(1)/(x-1))=

The value of L=lim_(x rarr0)((1)/(x))^(sin x)

Let L_(1)=lim_(x rarr0)((sin(2x)+cos(x)-1)/(x)) , L_(2)=lim_(x rarr oo)(sqrt(x^(2)-x)-x) , and L_(3)=lim_(x rarr4)(x^(2)-3x)/(x^(2)-x) , then the value of L_(1)L_(2)+(1)/(L_(3)) is

lim_(x rarr1)(x^((1)/(n))-1)/(x^((1)/(m))-1)(m and n are integers is equal

If the lim_(x rarr0)(1)/(x^(3))((1)/(sqrt(1+x))-(1+ax)/(1+bx)) exists and has the value equal to l, then find the value of (1)/(a)-(2)/(l)+(3)/(b)

If the lim_(x rarr0)(1)/(x^(3))((1)/(sqrt(1+x))-(1+ax)/(1+bx)) exists and has the value to 1,then find the value of (1)/(a)-(2)/(l)+(3)/(b)

If lim_(x rarr0)(sin^(-1)x-tan^(-1)x)/(3x^(3)) is equal to L ,then the value of (6L+1) is:

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

Let L=lim_(x rarr1)(sin(6cos^(-1)x))/(sqrt(1-x^(2))) and M=lim_(x rarr1)(1-cos(6cos^(-1)x))/(1-x^(2)) .Then value of L+M is

Let L= Lim_(x rarr-2)(3x^(2)+ax+a+1)/(x^(2)+x-2) .If L is finite,then a) L= 4/3 b) L=13 c) L=-2 d) L= -1/3