φ ′(x) ≠ 0 x0
,
, x0 .
x→x0 0; :
, .
( , )
47.
, ∞ / ∞.
f(x) φ(x) x0 ( x0),
,
0∙∞; ∞-∞; 1∞; ∞0; 00 .
, 0∙∞
f(x)→0, φ(x)→∞ →0
48. 2>x1, (2,x1)[a, b] f(2)>f(x1), y=f(x) . [a, b]. 2>x1, (2,x1)[a, b] f(2)<f(x1), y=f(x) . . : (a, b), f(x) , f(x)≤0 (a, b). : f(x) . (a, b) f(x)<0 (f(x)>0) (a, b), f(x)() (a, b).
49. 0 . y=f(x), . σ- 0, ≠ 0 f(2)<f(x0). .
50.
51. ab (M) (m) . , .
:1. ab. 2. . 3. . 4. (M) (m).
52. , 2 .
- , 1 , .
: , 2 <=0; , f``(x)>=0
: f``(x) -, ; f``(x)>0,
53. - , .
: X0 . , <=> `` = 0 0.
54. - , - , .
1) =0 - - f(x)=y, 0 |f(x)|+¥ ( x=b)
2) y=kx+b,,y=f(x) - -
lim[f(x)-(kx+b)]=0, f(x)=kx+b+a(...) - x¥ .
|
|
. ¥
f(x)/x=k+b/x+a/x, lim(f(x)/x)=limk+lim(b/x)+lim(a/x)
x¥,
k=lim(f(x)/x)
b=lim[f(x)-kx]
, kx+b=y
3)k=lim(f(x)/x)=0, y=b - .
55. -. -
- , - -
- - ,
-.
- (./):
f(-x)=x
f(-x)=-x (0,0)
-
-
-
-
-,
-
- - ,
- .