Pertanyaan

Jika diketahui x → 3 lim x 2 + 16 − 5 ax 2 − 9 a = 10 tentukan nilai a ?

Jika diketahui $x \to 3 lim \frac{ax ^{2} - 9 a}{x ^{2} + 16 - 5} = 10$ tentukan nilai $a$ ?

R. Novianto

Master Teacher

Mahasiswa/Alumni Universitas Tanjungpura Pontianak

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A

Pembahasan

Soal di atas adalah bentuk limit tak tentu dan dapat diselesaikandengandalil l'hospital dengan rumus : Maka kita dapat tentukan nilai a : Jadi,nilai adalah 1 Jadi, jawaban yang tepat adalah A

Soal di atas adalah bentuk limit tak tentu dan dapat diselesaikan dengan dalil l'hospital dengan rumus :

$begin mathsize 14px style limit as straight x rightwards arrow straight a of fraction numerator straight f open parentheses straight x close parentheses over denominator straight g open parentheses straight x close parentheses end fraction equals limit as straight x rightwards arrow straight a of fraction numerator straight f apostrophe open parentheses straight x close parentheses over denominator straight g apostrophe open parentheses straight x close parentheses end fraction end style$

Maka kita dapat tentukan nilai a :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as straight x rightwards arrow 3 of fraction numerator ax squared minus 9 straight a over denominator square root of straight x squared plus 16 end root minus 5 end fraction end cell equals 10 row cell limit as straight x rightwards arrow 3 of fraction numerator ax squared minus 9 straight a over denominator open parentheses straight x squared plus 16 close parentheses to the power of begin display style 1 half end style end exponent minus 5 end fraction end cell equals 10 row cell limit as straight x rightwards arrow 3 of fraction numerator 2 ax over denominator begin display style 1 half end style open parentheses straight x squared plus 16 close parentheses to the power of begin display style negative 1 half end style end exponent times 2 straight x end fraction end cell equals 10 row cell fraction numerator 2 straight a open parentheses 3 close parentheses over denominator begin display style 1 half open parentheses open parentheses 3 close parentheses squared plus 16 close parentheses to the power of negative 1 half end exponent times 2 open parentheses 3 close parentheses end style end fraction end cell equals 10 row cell fraction numerator 6 straight a over denominator begin display style 1 half end style open parentheses 25 close parentheses to the power of negative begin display style 1 half end style end exponent times 6 end fraction end cell equals 10 row cell fraction numerator 6 straight a over denominator 3 times fraction numerator 1 over denominator square root of 25 end fraction end fraction end cell equals 10 row cell fraction numerator 6 straight a over denominator begin display style 3 over 5 end style end fraction end cell equals 10 row cell 6 straight a cross times 5 end cell equals cell 10 cross times 3 end cell row cell 30 straight a end cell equals 30 row straight a equals cell 30 over 30 end cell row straight a equals 1 end table end style$

Jadi, nilai adalah 1

Jadi, jawaban yang tepat adalah A