Evaluate: `lim_(x->0)x^m(logx)^n ,m , n in Ndot`

Evaluate lim_(xto0^(+)) x^(m)(logx)^(m),m,n,inN.

Evaluate: lim_(x->a)(logx-loga)/(x-a)

lim_(x rarr 0)(x^(n) ln x), n gt 0

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

Evaluate: inta^(m x)b^(n x)dx

Evaluate the limit: lim_(x->1)("sin"(logx))/(logx)

Evaluate: lim_(x rarr 1) (e^(logx)-1)/(e^(x-1)-1)

IfI(m , n)=int_0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n (a) I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m-n))dx (b) I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m+n))dx (c) I(m , n)=int_0^oo(x^(n-1))/((1+x)^(m+n))dx (d) I(m , n)=int_0^oo(x^n)/((1+x)^(m+n))dx

If lim_(x->2)(x^n-2^n)/(x-2)=80 and n in N ,then find the value of n.

If lim_(n->oo)1/((sin^(-1)x)^("n")+1)=1 ,t h e n find the range of x.