推 mai911345:謝 59.113.20.40 07/20
※ 編輯: LuisSantos 來自: 61.66.173.21 (07/20 23:59)
※ 引述《mai911345 (mai911345)》之銘言：
: 10
: π/2 sin x
: 1.∫ ──────── dx
: 0 10 10
: sin x + cos x
: 1/x
: 2. lim x
: x→0 plus
: 謝謝~
π/2 (sinx)^10
1. 令 I = ∫ ------------------------- dx
0 (sinx)^10 + (cosx)^10
π/2 (sinx)^10
則 I = ∫ ------------------------- dx
0 (sinx)^10 + (cosx)^10
π/2 (cosx)^10
= ∫ ------------------------- dx
0 (sinx)^10 + (cosx)^10
π/2 (sinx)^10 + (cosx)^10 π/2 π
所以 2I = ∫ ------------------------- dx = ∫ 1 dx = ---
0 (sinx)^10 + (cosx)^10 0 2
π/2 (sinx)^10 π
所以 I = ∫ ------------------------- dx = ---
0 (sinx)^10 + (cosx)^10 4
2. 1/x
lim x
x→0+
1/x
= lim e^(lnx )
x→0+
lnx
= lim e^(-----)
x→0+ x
lnx
= e^( lim -----)
x→0+ x
= e^(-∞)
= 0
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 61.66.173.21