Pertanyaan

begin mathsize 14px style limit as x rightwards arrow infinity of invisible function application open parentheses square root of x squared plus 4 x plus 5 end root minus square root of x squared minus 2 x minus 3 end root close parentheses equals end style

B. Hary

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Menggunakan konsep mencari limit tak hingga dari fungsi akar. Jadi, jawaban yang benar adalah B.

Menggunakan konsep mencari limit tak hingga dari fungsi akar.

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of invisible function application open parentheses square root of x squared plus 4 x plus 5 end root minus square root of x squared minus 2 x minus 3 end root close parentheses end cell equals cell limit as x rightwards arrow infinity of invisible function application open parentheses square root of x squared plus 4 x plus 5 end root minus square root of x squared minus 2 x minus 3 end root close parentheses times 1 end cell row blank equals cell limit as x rightwards arrow infinity of invisible function application open parentheses square root of x squared plus 4 x plus 5 end root minus square root of x squared minus 2 x minus 3 end root close parentheses times fraction numerator square root of x squared plus 4 x plus 5 end root plus square root of x squared minus 2 x minus 3 end root over denominator square root of x squared plus 4 x plus 5 end root plus square root of x squared minus 2 x minus 3 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of invisible function application fraction numerator open parentheses square root of x squared plus 4 x plus 5 end root close parentheses squared minus open parentheses square root of x squared minus 2 x minus 3 end root close parentheses squared over denominator square root of x squared plus 4 x plus 5 end root plus square root of x squared minus 2 x minus 3 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of invisible function application fraction numerator x squared plus 4 x plus 5 minus open parentheses x squared minus 2 x minus 3 close parentheses over denominator square root of x squared plus 4 x plus 5 end root plus square root of x squared minus 2 x minus 3 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of invisible function application fraction numerator 6 x plus 8 over denominator square root of x squared plus 4 x plus 5 end root plus square root of x squared minus 2 x minus 3 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of invisible function application fraction numerator fraction numerator 6 x over denominator x end fraction plus 8 over x over denominator square root of x squared over x squared plus fraction numerator 4 x over denominator x squared end fraction plus 5 over x squared end root plus square root of x squared over x squared minus fraction numerator 2 x over denominator x squared end fraction minus 3 over x squared end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of invisible function application fraction numerator 6 plus 8 over x over denominator square root of 1 plus 4 over x plus 5 over x squared end root plus square root of 1 minus 2 over x minus 3 over x squared end root end fraction end cell row blank equals cell fraction numerator 6 plus 0 over denominator square root of 1 plus 0 plus 0 end root plus square root of 1 minus 0 minus 0 end root end fraction end cell row blank equals cell fraction numerator 6 over denominator 1 plus 1 end fraction end cell row blank equals cell 6 over 2 end cell row blank equals 3 end table$

Jadi, jawaban yang benar adalah B.