" 1."lim_(y rarr(1)/(2))[(1-8y^(3))/(y-4y^(3))]

Lim_(y rarr0)(a^(y)-a^(-y))/(y)

The value of lim_(x rarr1)(y^(3))/(x^(3)-y^(2)-1) as (x,y)rarr(1,0) along the line y=x-1 is

Let f(x)=cos((x)/(2))*cos((x)/(4))*...*cos((x)/(2^(n))). If lim_(n rarr oo)f(x)=g(x) and lim_(x rarr0)g(x)=k then value of lim_(y rarr k)[(1-y^(2011))/(1-y)]

lim_(x rarr0)((1-3x)^(40)*(5+y)^(10))/((3-2y^(2))^(25))2Lim

Solve : 8 ^(x+1) = 16 ^(y+2) and ( (1)/(2)) ^(3+x) = ((1)/(4))^(3y)

lim_(x rarr0)(1)/(x^(k+1))int_(0)^(x)(x^(k)+x^(k-1)y+x^(k-2)y^(2)+....+y^(k))f(y)dy=