Contoh Soal Limit Fungsi Matematika SMA

CONTOH SOAL LIMIT FUNGSI

1. 2. 3. 4. 5.

6. 7. 8.

   =  = ∞  =      = √   =  =  = √    √      √    =  =  = 3         =  =         =  =  (tak tentu)        =  =  Maka :           =    =  = 4           =   =         =    =        

0

Cara Horner :



x 2



x 2

9.

2

1

-4

↓ 2 3

1 -1 

2

3

-1

0

1

-5

2

2

1 -4

-2

↓

1

-4 -2

     



x -2



x -2

↓

4

=

  -4

2

0

1

1

↓

1

1

(selalu 0)

(+)

0 (selalu 0)

Cara Horner : 2

(+)

      

=

 

=

 

2

0 -2

(+)

1

(selalu 0)

0

-4 -4

-2

2

4

(+)

-1

-2

0

(selalu 0)

 10.   

=

   

=

 

=

 



=

 

Cara Horner :

 x 

↓

-1

8 -10 3

1

0

2

0

8

-6

4

-2

6

-3

2

0

3

(+)

0

6

0

(selalu 0)

   

=

 

 x  11.

2

↓

 

4

4 -3 0

Cara Horner :



x -2



x -2

12.

2

↓

4

  -4

0

2

0

-3

0 (selalu 0)

1

0

0

8

↓

  -2

1



x 3

13.

-1

-2

4 -8 4

 

=

  -3

-9

27 (+) 0

-3

-9

2

-6

-1

   √ 

 

6

 

=

-

(selalu 0)

3

0 -3

0 -1

=

=

27

-1

2

=

0 (selalu 0)

0

↓

 

(+)

0

↓

=

6 (+)

Cara Horner :



(selalu 0)

-3 -6

    x 3

(+)

(+)

0 (selalu 0)

 √    √  √  √     √     √     x

= = = =

 

=

 

=

 

 

14.

√    √ 

=

√    √  = =

=

x

√  √ 

x

√  √ 

(√ )   (√ ) (√ )   (√ ) (√ )   (√ ) 

 =   =       √  =  √  x √  x √  15.   √   √  √  √  =

16.

=

 (  ) √    (√ )

=

(√ )   (√ ) 

=

(√ )   (√ ) 

=

 

=

 

√    

     

Misal : x =

 = y

y 8=

 = 8

y =2

Soal Menjadi :

   

=

  =

17.

√     √  Misal : x =



 

√    



 = y

x 64 =

 = 64

y=4

Soal menjadi :

                     ()   (√ ) (√ )       x

=

18.

=

√    

   

Misal : x = X

 1 =

 = 1

Y =1

Soal menjadi :

   

=

 

=

 

Cara Horner :



1

x 1

19.

 

↓

1

0

0

0

0

-1

1

1

1

1

1 (+)

1

1

1

1

0 (selalu 0)

√ 



  

Misal : 3x-1 =

x 3=

 = 8

y =2

Soal menjadi :

      

=

          

4

=

   

=

   

=

  20.    √ 

  

Misal : 3x+2 = x 2=

 = 8

y =2

Soal menjadi :

        =

21.

=

()   

=

()   

=

 

√     √                   

=

 

Misal : x =

x 0=

 = 1

y =1

x=

Soal Menjadi :

=

22.

 

√ 



x

   

=

    

=

    

=

 

=

    

  

=

 

Misal :

         =

X+8

=

x

=

x 0=

 = 64

y

=4

Soal Menjadi :

()         =

 23.     

=

    

=

    

=

√  

  25.     

=

=

 

=

        

=

=

   

=

=

 24.   

x

         

 

=

4

         =

       

=

 

=

       

=

       

∞

 

=

 26.   √ 

27.

=

 

=

=

          

=

 √ 

 2√ 4 3 

=

=

 

 2 √ 4 3  =

               

=

          

=

 

=

x

√  √ 

   √      √ 

=

 √ 2 4 √ 2 3  =  √ 2  4 √ 2  3    =   √  √   =   √  √  =

0

        

=

28.

 

=

 √ 

x

√  √ 

  x

√  √  √  √ 

=

 √ 2 