Microsoft Word Formula kitobcha

Logarifmik funksiya

^{y } log_a^x

^{0  a  1}

1. 
   ^{Aniqlanish sohasi: D( y) } ^0; ^.
   
2. 
   ^{Qiymatlar sohasi: E( y) } ^{;} ^.
   
3. 
   ^{a  1 bo‘lsa,} ^0; ^{oraliqda o‘suvchi;}
   

^{0  a  1 bo‘lsa,} ^0;
oraliqda kamayuvchi.

4. 
   Grafigi (1;0) nuqtadan o‘tadi.
   

5. 
   Asimptotasi:
   

x  0 .


y  sin x

funksiya

1. 
   . Aniqlanish sohasi:
   
2. 
   . Qiymatlar sohasi:
   

D( y)  R .
E( y)  [1;1] .

3. 
   . Toq funksiya: sin( x)  sin x .
   

4. 
   . Eng kichik musbat davri:
   

T  2π .

5. 
   . Nollari: x₀  πn, n  Z .
   

6. 
   . Ishora o‘zgarmas oraliqlar:
   

^{x }^{2πn,π  2πn} ^{n  Z}


bo‘ lsa,


Sinx  0 ;

^{x }^{π  2πn, 2πn} ^{n  Z}
bo‘ lsa,
Sinx  0 .

7 . ^ ^π  2πn; ^π  2πn^
^{n  Z}
oraliqlarda o‘suvchi;

_ _{2 2} _

^π  2πn; ^3π  2πn^
^{n  Z}
oraliqlarda kamayuvchi.

_{ 2 2} _

8. 
   . Eng katta qiymati 1 :
   

Sinx  1  x  ^π
2

• 
  2πn,
  

n  Z .

8. 
   . Eng kichik qiymati  1 : Sinx  1  x   ^π
   

2

• 
  2πn, n  Z .
  

^{10 .} ^{2πn;π  2πn} ^{n  Z}
oraliqlarda qavariq;

^{π  2πn; 2π  2πn}
^{n  Z} ^{oraliqlarda botiq.}

y  cos x

funksiya

1. 
   . Aniqlanish sohasi:
   
2. 
   . Qiymatlar sohasi:
   

D( y)  R .
E( y)  [1;1] .

3. 
   . Juft funksiya: cos( x)  cos x .
   

4. 
   . Eng kichik musbat davri:
   

T  2π .

5. 
   . Nollari:
   

x  ^π
0 ₂

• 
  πn,
  

n  Z .

6. 
   . Ishora o‘zgarmas oraliqlar:
   

x ^  ^π  2πn, ^π  2πn ^
^{n  Z}
bo‘lsa,
Cosx  0 ;

 _{2 2} 
 

x ^{ π}  2πn, ^3π  2πn ^
^{n  Z}
bo‘lsa,
Cosx  0 .

 _{2 2} 
 

7. 
   ^. ^{π  2πn; 2πn} ^{n  Z} ^{oraliqlarda o‘suvchi;}
   

^{2πn; π  2πn} ^{n  Z} ^{oraliqlarda kamayuvchi.}

8. 
   . Eng katta qiymati 1 ,
   

Cosx  1 
x  2πn,
n  Z .

9. 
   . Eng kichik qiymati  1 , Cosx  1  x  π  2πn, n  Z .
   

10. .

• 
  ^π  2πn  x  ^π
  

 2πn
^{n  Z} 
oraliqlarda qavariq.

2 2
^π  2πn  x  ^3π

• 
  2πn
  

^{n  Z} 

oraliqlarda botiq.

2 2


y  tgx

funksiya

1. 
   . Aniqlanis h s ohas i :
   

x  ^π
2

• 
  πn,
  

n  Z .

2. 
   . Qiymatlar sohas i :
   

E( y)  R .

3. 
   . Toq funks iya :
   

tg(x)  tgx .

4. 
   . Eng kichik musbat davri: T  π .
   
5. 
   . Nollari: x₀  πn, n  Z .
   
6. 
   . Is hora o‘ zgarmas oraliqlar:
   

x ^πn, ^π  πn ^
^{n  Z}
bo‘ lsa,
tgx  0 ;

 ₂ 
 

x ^  ^π  πn,πn ^
^{n  Z}
bo‘ lsa,
tgx  0 .

 ₂ 
 

7. 
   . ^  ^π  πn; ^π  πn ^
   

^{n  Z} 
oraliqlarda o‘ s uvchi.

 _{2 2} 
 

8. 
   As imptotalari:
   

x  ^π
2

• 
  πn,
  

n  Z .

y  ctgx

funksiya

1. 
   . Aniqlanis h s ohas i :
   
2. 
   . Qiymatlar sohas i :
   

x  πn,
E( y)  R .
n  Z .

3. 
   . Toq funks iya :
   

ctg(x)  ctgx .

4. 
   . Eng kichik musbat davri: T  π .
   

5. 
   . Nollari:
   

x  ^π
0 ₂

• 
  πn,
  

n  Z .

6. 
   . Is hora o‘ zgarmas oraliqlar:
   

x ^πn, ^π  πn ^
^{n  Z}
bo‘ lsa,
сtgx  0 ;

 ₂ 
 

x ^  ^π  πn,πn ^
^{n  Z}
bo‘ lsa,
сtgx  0 .

 ₂ 
 

7. 
   ^. ^{πn; π  πn}^{, n  Z}
   

oraliqlarda ka mayuvchi.

8. 
   As imptotalari:
   

x  πn,
n  Z .

1. 
   . Aniqlanis h s ohas i :
   
2. 
   . Qiymatlar sohas i :
   

y  arcsin x


D( y)  [1;1] .
E( y)  ^ ^π ; ^{π } .

funksiya

_ _{2 2} _

3. 
   . Toq funks iya :
   

arcSin(x)  arcSinx .

4. 
   . Aniqlanis h s ohas ida o‘ s uvchi funks iya.
   

y  arccos x

funksiya

1. 
   . Aniqlanis h s ohas i :
   
2. 
   . Qiymatlar sohas i :
   

D( y)  [1;1] .
^{E( y) } ^0;π ^.

3. 
   . Toq ha m, juft ham e mas :
   

arcCos(x)  π  arcCosx .

4. 
   . Aniqlanis h s ohas idakamayuvchi funks iya.
   

y  arctgx

funksiya

1. 
   . Aniqlanis h s ohas i :
   
2. 
   . Qiymatlar sohas i :
   

D( y)  R .
E( y)  ^  ^π ; ^{π } .

 _{2 2} 

3. 
   . Toq funks iya :
   

 
arctg(x)  arctgx .

4. 
   . Aniqlanish sohasida o‘suvchi funksiya.
   

5. 
   . As imtotalari
   

y   ^π .
2
y  arcctgx

funksiya

1. 
   . Aniqlanish sohasi:
   

D( y)  R .

2. 
   . Qiymatlar sohas i :
   

^{E( y) }^0;π ^.

3. 
   . Toq ham emas, juft ha m e mas :
   

arcctg(x)  π  arcctgx .

4. 
   . Aniqlanis h s ohas ida kamayuvchi funks iya.
   
5. 
   As imptotalari y  0, y  π .
   

Hosila

y  f (x)

funksiyaning

x  x₀

nuqtadagi hosilasi

y^ 
f ^(x ) 
lim
y _

lim
f (x₀  x) 
f (x₀ )

⁰ xx_{0 x} xx_{0 x}