.


:




:

































 

 

 

 





.

1. f (x) 0 .

: (1)

a≠b. (2)

 

{ n} 0 ( n0),

 

, .. { f (n)} .

2. f (x) , .

. , . U1=(0-ε; 0+ε), ε>0. f (x) 1Î U1, │ f (1)│>1. U2=(0-ε/2; 0+ε/2), ε>0 , 2Î U2, │ f (2)│>2. , Un=(0-ε/n; 0+ε/n), f (n) > n, n0; f (n)→∞. .

3. 0 f (x) ≥b, . ( ).

4. 0 f (x)≥g(x), .

5. 0 f (x)≥g(x)≥h(x) f (x) h(x) → 0

 

 

.

 

 

.

. f (x) 0 , 0 {n}, n>0, {f(n)} .

:

.

= = f (x),

 

=+b = f (x) →+∞, f (x) f (x)= +b+α(),

 

. = f (x) →+∞ , ,

→-∞.

 

.

y=f(x) () . R1, 1, 2, , 1<2 -:

f(x1)<f(x2) (f(x1) >f(x2))

y=f(x) () . R1, 1, 2 1<2 -:

f(x1)≤f(x2) (f(x1) ≥f(x2))

, , - . .

.

.

1) lim f(x)sinx/x =1( →0) .

-. .. - y= sinx , , →0 1.

T

M

tgx

 

x

K A

O

MK= sinx , sinx<x<tgx,

1<x/ sinx<1/cosx

1>sinx/x>cosx

→0 lim cosx=1, lim 1=1. .

2) lim (1+1/x)x =e(→+ (-)∞) .

-.

1) +∞. . n, -:

n ≤ x< n+1 (1)

, >1,n>0. , : 1+1/ n ≥ 1+1/x> 1+1/(n+1)

(1), : (1+1/ n)n+1≥ (1+1/x)x> (1+1/(n+1))n f(x) ≥(1+1/x)x>g(x). →+∞,n →+∞, f(x) g(x)→. - - lim (1+1/x)x →( →+∞), ..

2) -∞. =-t, t>0.

(1+1/x)x=(1-1/t)-t =((t-1)/t)-t =(t/(t-1))t =(1+1/(t-1))t =(1+1/(t-1))t-1 (1+1/(t-1))x →*1= →-∞, .. t →+∞, ..





:


: 2016-10-30; !; : 450 |


:

:

- , - .
==> ...

782 - | 759 -


© 2015-2024 lektsii.org - -

: 0.009 .