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Nilai

Nilai begin mathsize 14px style limit as straight x rightwards arrow straight infinity of invisible function application open parentheses square root of 4 straight x squared plus 8 straight x end root minus square root of straight x squared plus 1 end root minus square root of straight x squared plus 3 straight 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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 begin mathsize 14px style limit as straight x rightwards arrow straight infinity of invisible function application open parentheses square root of 4 straight x squared plus 8 straight x end root minus 2 straight x plus straight x minus square root of straight x squared plus 1 end root plus straight x minus square root of straight x squared plus 3 straight x end root close parentheses equals 2 plus 0 plus open parentheses negative 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 bold lim with bold x rightwards arrow bold infinity below invisible function application open parentheses square root of bold ax squared plus bold bx plus bold c end root minus square root of bold px squared plus bold qx plus bold r end root close parentheses equals fraction numerator bold b minus bold q over denominator 2 square root of bold a end fraction end style 

Maka:

begin mathsize 14px style limit as straight x rightwards arrow straight infinity of invisible function application open parentheses square root of 4 straight x squared plus 8 straight x end root minus 2 straight x plus straight x minus square root of straight x squared plus 1 end root plus straight x minus square root of straight x squared plus 3 straight x end root close parentheses equals limit as straight x rightwards arrow straight infinity of invisible function application open parentheses square root of 4 straight x squared plus 8 straight x end root minus square root of open parentheses 2 straight x close parentheses squared end root plus square root of straight x squared end root minus square root of straight x squared plus 1 end root plus square root of straight x squared end root minus square root of straight x squared plus 3 straight x end root close parentheses end style 

 Penyelesaian bagian pertama :

begin mathsize 14px style limit as straight x rightwards arrow straight infinity of invisible function application open parentheses square root of 4 straight x squared plus 8 straight x end root minus square root of open parentheses 2 straight x close parentheses squared end root close parentheses equals limit as straight x rightwards arrow straight infinity of invisible function application open parentheses square root of 4 straight x squared plus 8 straight x end root minus square root of 4 straight x squared end root close parentheses equals fraction numerator 8 minus 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 limit as straight x rightwards arrow straight infinity of invisible function application open parentheses square root of straight x squared end root minus square root of straight x squared plus 1 end root close parentheses equals fraction numerator 0 minus 0 over denominator 2 square root of 1 end fraction equals 0 end style 

Penyelesaian bagian ketiga :

begin mathsize 14px style limit as straight x rightwards arrow straight infinity of invisible function application open parentheses square root of straight x squared end root minus square root of straight x squared plus 3 straight x end root close parentheses equals fraction numerator 0 minus 3 over denominator 2 square root of 1 end fraction equals negative 3 over 2 end style 

Jadi begin mathsize 14px style limit as straight x rightwards arrow straight infinity of invisible function application open parentheses square root of 4 straight x squared plus 8 straight x end root minus 2 straight x plus straight x minus square root of straight x squared plus 1 end root plus straight x minus square root of straight x squared plus 3 straight x end root close parentheses equals 2 plus 0 plus open parentheses negative 3 over 2 close parentheses equals 1 half end style 

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