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

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

If f(x) is a differentiable function for all x gt 0 and lim_(y to x)(y^(2)f(x)-x^(2)f(y))/(y-x)=2 , then the value of f'(x) is -

the value of lim_(x rarr y)(sin^(2)x-sin^(2)y)/(x^(2)-y^(2)) equals

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

lim_(x rarr 0) (x sqrt(y^(2) - (y - x)^(2)))/((sqrt(8xy - 4x^(2)) + sqrt(8xy))^(3)) equals :

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

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

lim_(y to 0) ((x+y)sec(x+y)-xsecx)/(y)

lim_(x rarr0)((x+y)sec(x+y)-x sec x)/(y) is equal to sec x(x tan x+1)(b)x tan x+sec xx sec x+tan x(d) none of these