Q.1.
(a) Determine if the following limits exist or not. If they do exist find the value of the limit.
(a, 1) \lim_{(x,y)\to(1,1)} \frac{(y-x)2y + 2(x-y)(y-2)}{4x^2-4y^2}
(a.2) \lim_{(x,y)\to(2,2)} 2x^2 - y(x+y) - (4x^2 - 4y^2)
(b) Define the concept of continuity and explain it using an appropriate diagram.
(c) Show that the polynomial function $f(x, y) = 2x^2 - y(x + y) - (x^2 - y^2)$ is continuous
at the point (2,4).
and find $\frac{\partial f(x,y)}{\partial x} = \lim_{h\to 0} \frac{f(x+h,y)-f(x,y)}{h}$ at the point (1,4).
(d) Using the same method, find $\frac{\partial f(x,y)}{\partial y}$.
