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Nilai

Nilai begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses x minus square root of x squared minus 5 x end root close parentheses equals... end style  

  1. undefined 

  2. begin mathsize 14px style 0 comma 5 end style 

  3. undefined 

  4. begin mathsize 14px style 2 comma 5 end style 

  5. begin mathsize 14px style 5 end style 

Jawaban:

Nilai limit tak hingga bentuk akar, dapat ditentukan dengan bentuk umum:

begin mathsize 12px style limit as x rightwards arrow infinity of open parentheses square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root close parentheses equals open curly brackets table attributes columnalign left end attributes row cell infinity comma space untuk space a greater than p end cell row cell fraction numerator b minus q over denominator 2 square root of a end fraction comma space untuk space a equals p end cell row cell negative infinity comma space untuk space a less than p end cell end table close end style  

Pada soal limit tak hingga bentuk akar belum sama dengan bentuk umum sehingga harus disamakan terlebih dahulu, diperoleh:

begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses x minus square root of x squared minus 5 x end root close parentheses equals limit as x rightwards arrow infinity of open parentheses square root of x squared end root minus square root of x squared minus 5 x end root close parentheses end style

Perhatikan bahwa nilai begin mathsize 14px style a equals p equals 1 end style, sehingga nilai limit tak hingga bentuk akar di atas dapat dicari seperti betiku:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as x rightwards arrow infinity of open parentheses x minus square root of x squared minus 5 x end root close parentheses end cell equals cell limit as x rightwards arrow infinity of open parentheses square root of x squared end root minus square root of x squared minus 5 x end root close parentheses end cell row blank equals cell fraction numerator b minus q over denominator 2 square root of a end fraction end cell row blank equals cell fraction numerator 0 minus open parentheses negative 5 close parentheses over denominator 2 square root of 1 end fraction end cell row blank equals cell 5 over 2 end cell row cell limit as x rightwards arrow infinity of open parentheses x minus square root of x squared minus 5 x end root close parentheses end cell equals cell 2 comma 5 end cell end table end style 

Jadi, jawaban yang tepat adalah D.

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