5.
1 / 3 MATHMEDIC .
101127 ( ) # 4636
, ?
y= ex (1, e) y= 2 x − k
k
1 e
1 2
e2
1 3
e4 1
4 1 + e
1 5
1 + e2 1
2
110921 # 4510
.
, .
f(x) = x − (a + 2)x + ax3 2 y= f(x)
(t, f(t)) y g(t) g(t)
(0, 5) a
151114 # 1377
. ,
.
,
.
, ?
[13 ∼ 14] a > 3 a y= ax−1 y= 3x
P P x k 13 14
P y= 3x x A P
y= ax−1 x B
H(k, 0) AH= 2BH a
1 6 2 7 3 8 4 9 5 10
161107 # 1460
,
?
y= 3ex−1 A O OA
1 6 2 7 3 2 2
4 3 5 10
5
160910 # 1433
y= ln 5x (51 ), 0 y ?
1 −
2
5 2 −2 3 −
2 3
4 −1 5 −
2 1
170611 # 1674
, ?
y= ln(x − 3) + 1 (4, 1) y= ax + b a, b a+ b
1 −2 2 −1 3 0 4 1 5 2
7
171115 # 1648
, .
?
y= 2e−x P(t, 2e )−t (t > 0) y
A P y B
APB t
1 1 2
2
e 3 2 4 2 5 e
3 / 3 MATHMEDIC .
181121 # 2284
,
.
.
.
?
t [1, ∞) f(x)
f(x) ={ln x
−t + ln x
(1 ≤ x < e) (x ≥ e)
g(x) y= g(x) h(t)
1 x (x − e){g(x) − f(x)} ≥ 0
h(t) a h(a) =
e+ 2 1 h′( ) × h (a)2e
1 ′
1 (e + 1)2
1 2
e(e + 1) 1
3 e2
1 4
(e − 1)(e + 1) 1
5 e(e − 1) 1
9
180616 # 1589
.
.
, ?
k f(x)
f(x) ={ x2+ k ln(x − 2)
(x ≤ 2) (x > 2)
t y= x + t y= f(x)
g(t) g(t) t = a a
k
1 −2 2 −
4
9 3 −
2 5
4 −
4
11 5 −3
1 . 2 . 13 3 . 4 . 5 .
6 . 7 . 8 . 9 .
