Question

微积分求大神解答，解题步骤尽量详细

Answer 1

f'x=3x²+6x-9=3(x-1)(x+3)
f'y=-3y²+6y=-3y(y-2)
极值f(1.0)，f(-3.0)，f(1.2)，f(-3.2)

Answer 2

∫∫D dσ/(1+x²+y²) D=｛(x，y)|x²+y²≤1｝
换成极坐标后原式=∫0→2π dθ∫0→1 rdr/(1+r²) ①
令r=tanα α[0，π/4]
①式=2π∫0→π/4 tanαdtanα/sec²α
=2π∫0→π/4 tanαdα
=2π∫0→π/4 sinα/cosαdα
=2π∫0→π/4 -1/cosαdcosα
=2π×[(-㏑|cosα|)|0→π/4]
=2π(-㏑1/2½ +㏑1)
=2π㏑2½
=π㏑2