Sinx ﺪﺣ - رشد

[Pages:5]sinx

x

x sinx x x

. 0 / 0 x = 0

. x sinx x

. ( ) x = y = 0 / 01745y y x 180

10 o , x = 0 /1745

sinx = 0 /1736,

5o ,

0 / 0873

2o ,

0 / 0349

1o ,

0 / 0175

0 / 0872, 0 / 0349, 0 / 0175,

sinx = 0 / 9948 x 0 / 9988 1/ 0000 1/ 0000

x 0 sinx / x 1

()

.

A C

0

B

BOC x

OBC = 1 ?1? sinx 2

OBC = 1 ? x 2

OBA = 1 ?1?tgx 2

0 < x < 2

sinx < x < tgx

sinx

1< x < 1 sinx cosx

cosx < sinx < 1

()

x

1-cosx = (1-cosx )1+ cosx = 1- cos 2x = sin 2x < sin 2x

1+ cosx 1+ cosx 1+ cosx sinx < x

1-cosx < x 2

()

1- x 2 < cosx

()

1- x 2 < sinx < 1

()

x

- < x < 0 0 < x < .

2

2

( ) .

-x 2

=

x

2

sin (-x (-x )

)

=

- sin x - x

= sinx x

x 2 sinx () () x . x < =

. x 0 1-cosx 0 () ( : x . x 0

sin ax ( x

tgx ( x

sinx

x (x -1) (

sin 2x (

x

( x) sinx ( x

x sinx (

1 - cosx 1 - 1 ( sinx tgx

sin ax (

sin bx 1 - 1 ( x tgx

x

? f (x ) = 1/ x x

. n 1/ n x .?

a x f (x ) : x f (x ) a

( ) K

f (x )-a <

. x > K

. 1/ K a = 0 f (x ) = 1/ x

x f (x ) a

:

f (x ) a

1/ x 0

:

x

x x

2 2

+x -x

+1 - 1

1

(

x x +1 1 ( x -1

x

x +1 x 2 +1

0

(

x sinx 0 ( x

. x

sinx (

cosx

x

x

sinx + cosx

0

(

. . ? x f (x ) ? (

. an f (x )

x n

x f (x ) .

x x > K x > K

?? . x < -K

:

x - x +

 ................
................

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