Let `g(x,y) = (e^(y) sin x)/x`, for `x ne 0` and g(0,0) =1. Show that g is continous at (0,0).

Let f(x,y) = (y^(2) -xy)/(sqrt(x)-sqrt(y)) for (x,y) ne (0,0) . Show that lim_((x,y) to (0,0)) f(x,y) =0

Let g(x,y) = (x^(2)y)/(x^(4) + y^(2)) for (x,y) ne (0,0) and f(0,0)=0. (i) Show that lim_((x,y) to (0,0)) g(x,y)=0 along every line y=mx, m in R . (ii) Show that lim_((x,y) to (0,0)) g(x,y) = k/(1+k^(2)) , along every parabola y=kx^(2), k in R{0} .

f (x) = (sin x )/(x) , x ne 0 and f(x) is continous at x = 0 then f(0) =

Let f(x) and g(x) be two equal real function such that f(x)=(x)/(|x|) g(x), x ne 0 If g(0)=g'(0)=0 and f(x) is continuous at x=0, then f'(0) is

Let f(x) and g(x) be two equal real function such that f(x)=(x)/(|x|) g(x), x ne 0 If g(0)=g'(0)=0 and f(x) is continuous at x=0, then f'(0) is

Let f (x+y)=f (x) f(y) AA x, y in R , f (0)ne 0 If f (x) is continous at x =0, then f (x) is continuous at :

Let f(x)=(sin x)/(x), x ne 0 . Then f(x) can be continous at x=0, if