arcsin
( ).
.
x = 0.
y = arccos x
.
m x,
y = cos x .
y = arccos x .
cos(arccos x) = x
arccos(cos y) = y
D (arccos x) = [ − 1;1], ( ),
E (arccos x) = [0;π]. ( ).
arccos
m α,
.
.
arctg
m x,
. .
0 < y < π,
arcctg
x.
cos x = 1, x = 2n; n 2 Z sin x = 1. x =/2+ 2n; n 2 Z tg x = 1. x =/4+ n; n 2 Z
cos x = -1, x = + 2n; n 2 Z: Sinx=-1, x = /2+ 2n; n 2 Z tg x =- 1. x = 4+ n; n 2 Z:
cos x = 0. x =/2+ n; n 2 Z Sinx=-0, x = n; n 2 Z: tg x = 0. x = n; n 2 Z:
2. , .
sin 2 x cosx 1 = 0.
3.
1) 2sinx 3cosx = 0
: cosx = 0, 2sinx = 0 sinx = 0 , sin 2 x + cos 2 x = 1. cosx ≠ 0 cosx.
, .
́ ,
1. (um)' = m um-1 u' (m R1 )
2. (au)' = au lna× u'.
3. (eu)' = eu u'.
4. (loga 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/ cos2u× u'.
9. (ctg u)' = - u' / sin2u
.
. x0 y=f(x)
y=f(x) x0:
.
x(t), :
()
,
[1] ().
()
,
[2] ().
.
,
|
|
.
[2; 0,5].
.
.
́́ [1] ( . ασϋμπτωτος , )
, ,
[2]
.
.
1.
2.
. :
1) y () =0 y () =¥;
2) , ,