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15.

, , .
y=f(x),- .x₀, - - . (1) (1) 3- :

1)-

2)- f(x) lim x

3)lim f(x) .=

y=f(x) (a;b) .o . x , .

, -

2

(1) :

(2)

. - y=f(x), ., . (2),. -

- y=f(x),- (a;b), . .
y=f(x),- [a;b], (a;b) . X=a , .x=b
- - -. x= x₀,-. , 3 ..

16.

=, -, = -, 3- .

-
. - . 1- 2- .
. x₀-. 1 , - y=f(x), . , :
) ₁=₂, x₀ - .
) A₁≠A₂, x₀ - . . - |₂-₁|, -, . 1 .

., x₀ - . 2 - y=f(x) 1 =∞ .

17. -.
1. 2 .
2. - u= . x₀, - y=f(u) . u₀=ϕ(x₀) - y=(ϕ(x))- . x₀
3. - .

 

18.

.

.

t OM=S. s=s(t). .

.

, . . t( )

L 2 M . . L ., . . . , . , . .

- y=f(x).

,

,. ., . ,

=
19.

, . .
- y=f() (a;b)
1. ͼ(a;b) , 2. . - y. ∆y=f(x+∆x)-f(x)
3...
4. . ∆->0

, - - f(x) f, f (x),y(x) ..
= f (x)
- y=f(x) . , - , .

-. - y=f(x) .(a;b), (;b)

. .y`(Xo);

v`(t)=

t S t- .

.

K=f`(x)

- .= - .- .?????

.
: - - ,

: - .

20.

.
- u=u(x),v=v(x)
1.(vu)ˈ=(uˈvˈ)
2.(uv)ˈ=uˈv+vˈu (cuˈ)cuˈ -
3.()ˈ=

4.
y=f(u) u=ϕ(x)

yᵪˈ=yˈᵤ Uₓ

5. - -:

y=f(x), x=ϕ(y)

yₓˈ=

1.(c)ˈ=0 c-const

2.()ˈ=

2. (a u)' = a u lna ×u'.

3. (e u)' = e u u'.

4. (log a u)' = u' /(u ln a).

5. (ln u)' = u'/u.

6. (sin u)' = cos u ×u'.

7. (cos u)' = - sin u ×u'.

8. (tg u)' = 1/ cos 2 u ×u'.

9. (ctg u)' = - u' / sin 2 u.

10. (arcsin u)' = u' / .

11. (arccos u)' = - u' / .

12. (arctg u)' = u' /(1 + u 2).

13. (arcctg u)' = - u' /(1 + u 2).

21.

, - - y=f(x), . , - . - - . . . - F(x;y)=0 . - . - .





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: 2015-11-23; !; : 672 |


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