If(z)- 니 < e. By definition Show that: lim, »1+i = - а. b. 4 lim = 2i. %3D 2- 1-i z2
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- If x and y are elements of an ordered integral domain D, prove the following inequalities. a. x22xy+y20 b. x2+y2xy c. x2+y2xyThe paraboloid z = x2 + y2 - 4x + 2y + 5 has a local minimum at (2, -1). Verify the conclusion of as shown for this function.Let y(t) be the solution of dy/dt = 0.3y(2 − y) with y(0) = 1. Determine limt→∞ y(t) without solving for y explicitly.
- Show that the function f (x, y)=(2 + x-y) / [1+ 2x ^ 2)+(3y ^ 2)] ∈R has a limit at (0,0).Evaluate∮C (x + 3y)dx + ydy where C is the Jordan curve given by thegraphs of y = e^x, y = e^−x and the horizontal line y = e^−1a) By Green’s theoremb) By direct computationFind dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before differentiating. w = x2 + y2 + z2, x = cos t, y = sin t, z = et