Show that the function f defined by (r, y) = (1, –1) (r, y) # (1, –1) f(r, y) = 1² + y is not continuous at (1,-1).
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- If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?Suppose that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. What is the value f(2, 3)?Show that the function f(z)=sin x cosh y+i cosx sinh y is continious as well as analytic every where.
- Show that f(z) =xy+iy is everywhere continuous but is not analyticAssume that f : (0, 1) → R is a differentiable function with the derivative f' increasing on (0, 1). Prove that f' is continuous on (0, 1).Let ƒ(x, y) =(x2-y2)/(x2+y2) for(x, y) ≠ (0, 0). Is it possible to define ƒ(0, 0) in a way that makes ƒ continuous at the origin? Why