Evaluate: `("lim")_(xvec0xvec0)(y^2+sinx)/(x^2+siny^2)` where `(x , y)vec(0,)` along the curve `x=y^2`

Q.lim_(x rarr0,y rarr0)(y^(2)+sin x)/(x^(2)+sin y^(2)), when (x,y)rarr(0,0) along the curve x=y^(2) is

Evaluate: (lim)_(xvec 0)(log(5+x)-log(5-x))/(x)

The value of ("lim")_(xvec0)(e^(2x)-cos x-"ln"(1+2x))/(xtanx-sinx)i s 0 (b) 1 (c) 2 (d) 3

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

A curve satisfies the differential equation (dy)/(dx)=(x+1-xy^(2))/(x^(2)y-y) and passes through (0,0)(1) The equation of the curve is x^(2)+y^(2)+2x=x^(2)y^(2)(2) The equation of the is a tangent to curve (4)y=0 is a tangent to curve

Find the area bounded by the curves x+2|y|=1 and x=0

Which of the following limits tends to unity? (a) ("lim")_(xvec0)sin(tanx)/(sinx) (b) ("lim")_(xvecpi/2)sin(cosx)/(cosx) ("lim")_(xvec0)"sin"(e^x-1)/x (d) ("lim")_(xvec0)(sqrt(1+x)-sqrt(1-x))/x

if y=(1)/(2)sin^(-1)((2xy)/(x^(2)+y^(2))) and y

(dy)/(dx) + 2y = e ^(-2x) sinx , given that y=0 when x = 0