`lim_(y rarr x) (y^x - x^x)/(y-x)`

lim_(y rarr x)((y^(y)-x^(x))/(y-x))=

lim_ (y rarr x) (y cos xx cos y) / (yx)

lim_(x rarr 0) x^2/y = 0

lim_(x rarr y) (tanx-tany)/(x-y)=

lim_(x rarr0)(|x|)/(x)

the value of lim_(x rarr y)(x^(y)-y^(x))/(x^(x)-y^(y)) is:

Evaluate: lim_(x rarr0)(y^(2)+sin x)/(x^(2)+sin y^(2)) where (x,y)rarr(0,) along the curve x=y^(2)

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)]

If f(x) + f(y) = f((x+y)/(1-xy)) for all x, y in R (xy ne 1) and lim_(x rarr 0) (f(x))/(x) = 2 , then

lim_(x rarr0)(x sqrt(y^(2)-(y-x)^(2)))/({sqrt(8xy-4x^(2))+sqrt(8xy)}^(3))=