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Тригонометриялық теңдеулер

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Тригонометриялық теңдеулер

 егер

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y =tgxфункциясы

1.y=3tg(

1)

2.мәндер облысы Е(y)=R

3. ең кіші оң периоды 2

4 .y=3tg(

 

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y=ctgx функциясы

1.y=-2ctg(

1)анықталу облысы ;

2)мәндер облысы Е(y)∊R

3)

4)y=F(–x)= –2ctg(  – функция жұп та, тақ та емес.

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Тригонометриялық теңдеулер Тригонометриялық теңдеулер

Жаңа айнымалы енгізіп шығарамыз

si

2si

2(1–

2– 2

–2co

2 cosx=t

2

D=25-4

=[

                             x=2 z ж; 2

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Тригонометриялық теңдеулер жүйесі

Тригонометриялық теңдеулер жүйесі

1.+ -

Sinxsiny+cosxcosy= cosxcosy–sinxsiny=0

cos(x–y)=                                      cos(x+y)=0

                                                      2x=

                                                      X=

2y=

y =

 

 

1)                                               2)

3)                                        4)

5)                                   6)           

7)                                         

 

8)

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15)                                          16)

17)                                          18)

19)

20

 

Тригонометриялық теңсіздіктер

1)                1)                    1)

2)               2)                    2)

3)               3)                    3)

4)                 

5)                    6)

7)                              9)

10)                        12)

13)           14)                

 

16)                          18)

19)                             21))

22)                         

24)

25) 0

26)

 

 

Функцияның нүктедегі шегі туралы ұғым және функцияның үзіліссіздігі

Мысалы :1  y = F(x) функциясының х нүктесі 4ке ұмтылғандағы (  мәнін анықтайық :

F(x)=2-  lim F(x) =2- =-14

2 . F(x)=

= = =

1. F(x)= 5x+2. x

2. F(x)=

3. F(x)= 4x ­­­ 1. x

4. F(x)= 3- . x

5. F(x) =

6. F(x)=

7. F(x)=

8. F(x)= x

9. F(x)= 1 x x

10. F(x)=2+x x  

1. F(x)= x  

2. F(x) =   x

3. F(x)= x

4. F(x)= x

5. F(x)= x

6. F(x)= x

 

1. F(x)=2x+1 x

2. F(x)= 3x-1 x

3. F(x)= x

4. F(x)= x

5. F(x)= x

6. F(x)= x

 

                

                    

                   

                   

               

                 

                

                   

                    

                   

 

                                          

 

Туынды

(u+v)'=u'+v '                                (c

(u                  ( )'=n                    ( )'=

1. y′=(5x+1)′=(5x)

2. y′=( =6 =24

3. y′=(8

4. y′=(2 =(2

5. y′=[(2+x)(2x-1)]′=(2+x)′

6. y′=( )′= = = =

7.y= ) = = = = = =

1. y=2+x

2. y=

3. y=6x

4. y=5x+1

5. y=2+

6. y= +1

7. y=0.4x

8. y=10+x

9. y=100x

10. y=4x-0.5

11.y= +2x-1

12. y= -4x+5

13.y= - + -x

14.y= - +13x-1

15. y= +8x+2

16.y=(x+2)(x-1)

17.y=                

18.y= -

19.y=      

20.y=               

21.y= - + +3x

22.y=               

23. y= - + -23

1.y=

2.y=

3.y=

4.y=

5.y=

6.y=

7.y=

8.y=

9.y=

10.y=

11.y=

12.y= - +1

13.y= -2x+1

14.y=1+x-

15. -3x+1

16.y=(x+4)(2x+1)

17.y=(3x-2)(5x+1)  

18.y=3x

19.y=(3+x)( -1)

20.y=( +1)(3+

21. y=

22.y=              23.y=

1.y=2x-1

2. y =-0.5x+0.5

3. y =4x-

4. y =13x+2

5.y=0.7x-4

6.y= x

7. y =- x+3         

8.y= 3x-0.5

9.y= ­-4x+0.1     

10.y=13x-1   

11.y=               

12.y=

13. y=          14.y= + -9x+1

15.y=           16.y= - -

17.y=                  

17.y=(3x-5)(3x+1)  

18.y=(1+2x)(1-2x)  

19.y=( +1)(2-x)    

21.y= -

Туындының физикалық және геометриялық мағынасы

A(t)=v'(t)= s''(t) немесе v(t)=s'(t) физикалық мағынасы

F''( )=tga=k геометриялық мағынасы

y=f( )+F'( (x- ) жанаманың теңдеуі

Мысалы;

1) s(t)= +2 t=5 v=? a=?

V(t)=S'(t)=( +2)'=2t. a(t)=v'(t)=(2t)'=2.

V(t)=2*5=10м/с Ж: (v)=10м/с, a=2м/

3) y= . N(1. 1) . a=? y'=2x f'(1)=2*1=2=tga a=arctg2

4) x(t)=

 

A(t)=  

5)x(t)=9

 

A(t)=  

6)F(x)=

F′(x)=(

Tg    tg

7)F(x)=2

F′(x)=(2

Tg   tg

1. x(t)= +3 t=4c v=?



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