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Nilai

Nilai begin mathsize 14px style lim with x yields infinity below invisible function application open parentheses square root of 4 x squared plus 8 x end root minus sign square root of x squared plus 1 end root minus sign square root of x squared plus 3 x end root close parentheses equals horizontal ellipsis. end style 

  1. begin mathsize 14px style 5 over 2 end style 

  2. begin mathsize 14px style 2 end style 

  3. begin mathsize 14px style 3 over 2 end style 

  4. begin mathsize 14px style 1 end style 

  5. begin mathsize 14px style 1 half end style 

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A. Nadhira

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style lim with x yields infinity below invisible function application open parentheses square root of 4 x squared plus 8 x end root minus sign 2 x and x minus sign square root of x squared plus 1 end root plus x minus sign square root of x squared plus 3 x end root close parentheses equals 2 plus 0 plus open parentheses negative sign 3 over 2 close parentheses equals 1 half end style  

Pembahasan

Ingat kembali rumus limit berikut : Maka: Penyelesaian bagian pertama : Penyelesaian bagian kedua : Penyelesaian bagian ketiga : Jadi,

Ingat kembali rumus limit berikut :

begin mathsize 14px style lim with x yields infinity below invisible function application open parentheses square root of ax squared plus bx and c end root minus sign square root of px squared plus qx and r end root close parentheses equals fraction numerator b bond q over denominator 2 square root of a end fraction end style 


Maka:

begin mathsize 14px style lim with x yields infinity below invisible function application open parentheses square root of 4 x squared plus 8 x end root minus sign 2 x and x minus sign square root of x squared plus 1 end root plus x minus sign square root of x squared plus 3 x end root close parentheses equals lim with x yields infinity below invisible function application open parentheses square root of 4 x squared plus 8 x end root minus sign square root of open parentheses 2 x close parentheses squared end root plus square root of x squared end root minus sign square root of x squared plus 1 end root plus square root of x squared end root minus sign square root of x squared plus 3 x end root close parentheses end style  
 

Penyelesaian bagian pertama :

begin mathsize 14px style lim with x yields infinity below invisible function application open parentheses square root of 4 x squared plus 8 x end root minus sign square root of open parentheses 2 x close parentheses squared end root close parentheses equals lim with x yields infinity below invisible function application open parentheses square root of 4 x squared plus 8 x end root minus sign square root of 4 x squared end root close parentheses equals fraction numerator 8 minus sign 0 over denominator 2 square root of 4 end fraction equals 8 over 4 equals 2 end style 
 

Penyelesaian bagian kedua :

begin mathsize 14px style lim with italic x yields italic infinity below invisible function application open parentheses square root of italic x squared end root minus sign square root of italic x squared plus 1 end root close parentheses equals fraction numerator 0 minus sign 0 over denominator 2 square root of 1 end fraction equals 0 end style 
 

Penyelesaian bagian ketiga :

begin mathsize 14px style lim with x yields infinity below invisible function application open parentheses square root of x squared end root minus sign square root of x squared plus 3 x end root close parentheses equals fraction numerator 0 minus sign 3 over denominator 2 square root of 1 end fraction equals minus sign 3 over 2 end style 
 

Jadi, begin mathsize 14px style lim with x yields infinity below invisible function application open parentheses square root of 4 x squared plus 8 x end root minus sign 2 x and x minus sign square root of x squared plus 1 end root plus x minus sign square root of x squared plus 3 x end root close parentheses equals 2 plus 0 plus open parentheses negative sign 3 over 2 close parentheses equals 1 half end style  

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