Question

16

作業寫不出來😭微積分

if (x, y) = (0,0)
( 20 points ) Let f(x, y) =
x²y²
x4 + y +
0,
if (x,y) = (0,0)
(a) Does
lim
f(x,y) exist ? Give reasons.
(x,y) → (0,0)
(b ) Find the partial derivatives fx(0,0) and fy(0,0).

( 20 points ) Determine whether the series is convergent or divergent.
Vn+1-vn
(a) En=1
(b) An= 1 zinn
Vn2 + 1

(15 points ) Let R be the region bounded by the parabola x = y, x + y = 4, and x = 0.
(a)(6 points ) Sketch the region R.
(b) Find the double integral of f(x, y) = 2x + 2y – 1 over R.

calculus