Nilai x→−5lim x+51−x+6 adalah....

Pertanyaan

Nilai $begin mathsize 14px style limit as x rightwards arrow negative 5 of space fraction numerator 1 minus square root of x plus 6 end root over denominator x plus 5 end fraction end style$ adalah....

L. Indah

Master Teacher

Mahasiswa/Alumni Universitas Siliwangi

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Nilai limit pada soal di atas dapat dicari dengan cara mengalikannya dengan akar sekawan dari yaitu . Diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 5 of fraction numerator 1 minus square root of x plus 6 end root over denominator x plus 5 end fraction end cell equals cell limit as x rightwards arrow negative 5 of open parentheses fraction numerator 1 minus square root of x plus 6 end root over denominator x plus 5 end fraction times fraction numerator 1 plus square root of x plus 6 end root over denominator 1 plus square root of x plus 6 end root end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow negative 5 of fraction numerator 1 minus left parenthesis x minus 6 right parenthesis over denominator open parentheses x plus 5 close parentheses open parentheses 1 plus square root of x plus 6 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow negative 5 of fraction numerator negative left parenthesis x plus 5 right parenthesis over denominator open parentheses x plus 5 close parentheses open parentheses 1 plus square root of x plus 6 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow negative 5 of open parentheses negative fraction numerator 1 over denominator 1 plus square root of x plus 6 end root end fraction close parentheses end cell row blank equals cell negative fraction numerator 1 over denominator 1 plus square root of negative 5 plus 6 end root end fraction end cell row blank equals cell negative 1 half end cell end table end style$

Dengan demikian, jawaban yang benar adalah B.