Evaluate: `lim_((x,y)->(0,0))(x^(3)y)/(x^(4)+y^(4))`

Evaluate lim_(yto0)(y^(2)+sin x)/(x^(2)+siny^(2)), where (x,y)to(0,0) along the curve x=y^(2) .

Evaluate: ("lim")_(x→0,y→0)(y^2+sinx)/(x^2+siny^2) where (x , y)→(0,0) along the curve x=y^2

If the equation of the normal to the curve y=f(x) at x=0 is 3x-y+3=0 then the value of lim_(xrarr0) (x^(2))/({f(x^(2))-5f(4x^(2))+4f(7x^(2))}) is

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

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

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

If x ne 0 and (x^(4))(x^(-4))=y, what is y?

Find the centre and radius of each of the following circle : (i) x^(2)+y^(2)+4x-4y+1=0 (ii) 2x^(2)+2y^(2)-6x+6y+1=0 (iii) 2x^(2)+2y^(2)=3k(x+k) (iv) 3x^(2)+3y^(2)-5x-6y+4=0 (v) x^(2)+y^(2)-2ax-2by+a^(2)=0

Solve for x and y : (2)/(x) + (3)/(y ) = 13, (5)/(x) - ( 4)/( y) = - 2 ( x ne 0 and y ne 0 )

Solve for x and y : (2)/(x) + (3)/(y ) = 13, (5)/(x) - ( 4)/( y) = - 2 ( x ne 0 and y ne 0 )