: .
: .
: .
( ): .
: .
: .
: .
: .
:
. :
( ), .
28.
, .
y = f(x) (a, b), x0. x0 f '(x0). x = g(y) y0 = f(x0), .
, (sin2x+cos2x=1 → cos2x=1-sin2x) =
= {cosx=V ̄1-sin2x, xϵ(-π/2; π/2} = 1/V ̄1-sin2x = {x=arcsiny} = 1/V ̄1-sin2(arcsiny) = {sin(arcsiny)=a} = 1/V ̄1-y2. (arcsiny) = 1/V ̄1-y2.
y x arcsinx = 1/V ̄1-x2.
30.
.
f (x) [ a, b ], , Î (a, b), f (b) − f (a) = f '(c)(b − a). y=f(x)
, A B, . , , :
,
.
, :
F(x):
, .
32.
. .
, .
x = f(t) t, y = f(x) x = f(t). y = f(f(t)) t,
(f(f(t)))' = f'(x)f'(t).
34.
. . .
y=f(x) 0 ∆ 0.
dy = f(x0)∆x (∆x= dx)
dy = f(x)dx, y . → dsinx = dcosxdx
36.