Pertanyaan

x → 3 lim x 2 − 5 − 2 x 2 − 9

$x \to 3 lim \frac{x ^{2} - 9}{x ^{2} - 5 - 2}$

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

adalah .

$limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator square root of x squared minus 5 end root minus 2 end fraction$ adalah

Pembahasan

Mencari nilai limit dengan menggunakan faktor dan akar sekawan. Berlaku aturan : Sehingga : Jadi, adalah .

Mencari nilai limit dengan menggunakan faktor dan akar sekawan. Berlaku aturan :

Sehingga :

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator square root of x squared minus 5 end root minus 2 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis x plus 3 right parenthesis over denominator square root of x squared minus 5 end root minus 2 end fraction times fraction numerator square root of x squared minus 5 end root plus 2 over denominator square root of x squared minus 5 end root plus 2 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis x plus 3 right parenthesis left parenthesis square root of x squared minus 5 end root plus 2 right parenthesis over denominator open parentheses square root of x squared minus 5 end root close parentheses squared minus open parentheses 2 close parentheses squared end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis x plus 3 right parenthesis left parenthesis square root of x squared minus 5 end root plus 2 right parenthesis over denominator x squared minus 5 minus 4 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis x plus 3 right parenthesis left parenthesis square root of x squared minus 5 end root plus 2 right parenthesis over denominator x squared minus 9 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator up diagonal strike left parenthesis x minus 3 right parenthesis left parenthesis x plus 3 right parenthesis end strike left parenthesis square root of x squared minus 5 end root plus 2 right parenthesis over denominator up diagonal strike left parenthesis x minus 3 right parenthesis left parenthesis x plus 3 right parenthesis end strike end fraction end cell row blank equals cell limit as x rightwards arrow 3 of left parenthesis square root of x squared minus 5 end root plus 2 right parenthesis end cell row blank equals cell square root of 3 squared minus 5 end root plus 2 end cell row blank equals cell square root of 9 minus 5 end root plus 2 end cell row blank equals cell square root of 4 plus 2 end cell row blank equals cell 2 plus 2 end cell row blank equals 4 end table$

Jadi, $limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator square root of x squared minus 5 end root minus 2 end fraction$ adalah .