ネピアの 2 - keio universityweb.econ.keio.ac.jp/staff/tose/cours/2020/calcnt/calcnt... · 2020....

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ネピアのॐ Q kpBfi„fiea 'o¢P bfilQ …WL ‹…qm kpBfi„fiea 'o¢P ネピアのॐ Q q § qm 8 5 Part 0 2 .

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8 5 Part 0 2 .
L2TB2`b LmK#2` L2TB2`b LmK#2`
2R =
R +
2.to ei ( → e
.
y R k · · · M M+R . . .
{M} J > y
M J (M = y, R, k, j, . . . )
{M}
h?2 T`QQ7 Q7 i?2 i?2Q`2K Bb ?B;?Hv i`Mb+2M/2MiHX q2 `2 ;QBM; iQ rQ`F QM i?2 bbmKTiBQM Q7 BiX
LQ#mvmFB hPa1 2 j f RN
→ R .
_
t.IT
R Mk + M*j
R Mj + · · ·+ M*F
Mk + M(M R)(M k)
j · k · R · R Mj + . . .
· · ·+ M(M R)(M k) · · · (M F + R) F(F R) · · · k · · · R · R
MF + · · ·+ R MM
i-"

ii.Tttfs
ostream:
n. i ) -.- ) )

2M UkV
1 Times
2M < R + R + R k! +
R j! + · · ·+ R
R · k · k . . . k < R · k · j . . . M

R kk + · · ·+ R
i - -
L
*QMp2`;2M+2 Q7 2M U9VMQi?2` TT`Q+?
h?2 @: AM2[mHBiv 6Q` (M + R) TQbBiBp2 MmK#2`b R, k, . . . , M+R > y- r2 ?p2
(Rk . . . M+R) R
M+R R + · · ·+ M+R M + R
q2 TTHv i?2 BM2[mHBiv iQ i?2 (M + R) MmK#2`b
R + R M
M ·R R
R+ R
M + R LQ#mvmFB hPa1 2 d f RN

*QMp2`;2M+2 Q7 2M U8VMQi?2` TT`Q+?
hFBM; i?2 (M + R)i? TQr2` Q7 i?2 #Qi? bB/2- r2 ;2i
R + R M
M+R BX2X 2M 2M+R
++Q`/BM;Hv {2M} Bb BM+`2bBM;X q2 /2}M2 MQi?2` b2[m2M+2 {7M} #v
7M =
R +
R +
*QMp2`;2M+2 Q7 2M UeVMQi?2` TT`Q+?
q2 KF2 mb2 Q7 i?2 : BM2[mHBiv 7Q`
R R M
M ·R R
R R
M M + R
hFBM; i?2 (M + R)i? TQr2` Q7 i?2 #Qi? bB/2- Bi 7QHHQrb i?i
R R M
*QMp2`;2M+2 Q7 2M UdVMQi?2` TT`Q+?
JQ`2Qp2` r2 iF2 i?2 BMp2`b2 Q7 i?2 #Qi? bB/2 iQ ;2i
7M =
R +
++Q`/BM;Hv
LQ#mvmFB hPa1 2 Ry f RN
URV
R ` > y 9 R
R +
R +
` Rk
Rk
R +
` je8
je8
i
UkV
*QKTQmM/BM; Q7 i?2 BMi2`2bi BM ;2M2`H K
R +
lim K!+1
-
R + R
R M
Lecob Pat 3. 2)
-_-

-
R + R i
pe
[ ' → e )
2
N = max (N . . Ne) Tt
Nz
.
/ ~
b i = b i ! 1 b ! +1
R + R i
S - 1→ tofeehse~ESI.io = 1 .
U9V
? ! +y- i ! +1
(R + ?) R ? = (R +
- T
i!+ 7 (i)
UBBV lim i!++y
7 (i)
7 (i)
lim i!++y
, " > y > y
+ < i < + + ) ↵ " < 7 (i) < ↵+ " LQ#mvmFB hPa1 2 Rd f RN
VfB 9'1
T hii
Jlt ) → d (t → et o ) E> o Spo J (t) -) C t → c_ o ,
C < t < et S
E -→ X- {< J ( t) <ateIn
1 !
t = c Ct 81
U8V
LQ#mvmFB hPa1 2 R3 f RN
J ) = t o t.vn → to J (tu) -) f ( to)
1
.
UeV t = log(R + ?)
? = 2t R
t ! y ? ! y
LQ#mvmFB hPa1 2 RN f RN
:

-
ER
U = logt du