2010 -2011 d℄WXd^W 31 Va[� 6 e 16 _ §1-§2 8:00-9:30

0. �S�>DK�:�:+����C"(;�O�-*6�;5?�1. ` �: y = f(x) L� a ��$I F�0 f(0) = 0, P.

limn→∞

n∑

k=1

f(k

n2) =

1

2f ′(0). b�'G�: f(x) L x = 0 � Taylor N%8�

2. ` y = f(x) L (−∞, +∞) R)C�0 limx→0

f(x)

x= A. , Φ(x) =

∫

1

0f(xt)dt,1��

limx→0

Φ(x)

x. b�< lim

x→0

f(x)

x= A, E=T f(0) = 0, 0 f ′(0) = A. 4�! Φ(x) B�

Φ(x) =1

x

∫

x

0

f(u)du x 6= 0,G l’Hospital �M�3. f\ ��

limn→∞

( 1

n + 1+ · · · +

1

2n

)

= ln 2.ZY 1 'G7;#�1

2+

1

3+

1

2+

1

n− ln n = γ + o(1) n → ∞/R γ 9 Euler �:�ZY 2 !�8

1

n + 1+ · · · +

1

n + n�B��: y = 1

1+xL2� [0, 1] 7 n ��? Riemann ��

n∑

k=1

1

1 + k

n

1

n,/R 1

nAJ △xk, ÆR��Q3U ξk = k

n, HJ y = 1

1+xL [0, 1] &�����&�� ��

1