Pertanyaan

x → 3 lim x 2 + 9 x − 36 x 2 − x − 6 = ....

$x \to 3 lim \frac{x ^{2} - x - 6}{x ^{2} + 9 x - 36} =$ ....

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Perhatikan bahwa jika dilakukan substitusi x = 3 , maka didapatkan hasil . Sehingga perlu dicari cara lain untuk mencari nilai limitnya. Perhatikan bahwa Jadi, jawaban yang tepat adalah E.

Perhatikan bahwa jika dilakukan substitusi x = 3, maka didapatkan hasil .
Sehingga perlu dicari cara lain untuk mencari nilai limitnya.

Perhatikan bahwa

$begin mathsize 14px style limit as straight x rightwards arrow 3 of square root of fraction numerator straight x squared minus straight x minus 6 over denominator straight x squared plus 9 straight x minus 36 end fraction end root equals square root of limit as straight x rightwards arrow 3 of fraction numerator straight x squared minus straight x minus 6 over denominator straight x squared plus 9 straight x minus 36 end fraction end root equals square root of limit as straight x rightwards arrow 3 of fraction numerator open parentheses straight x minus 3 close parentheses open parentheses straight x plus 2 close parentheses over denominator open parentheses straight x minus 3 close parentheses open parentheses straight x plus 12 close parentheses end fraction end root equals square root of limit as straight x rightwards arrow 3 of fraction numerator straight x plus 2 over denominator straight x plus 12 end fraction end root equals square root of fraction numerator 3 plus 2 over denominator 3 plus 12 end fraction end root equals square root of 5 over 15 end root equals square root of 1 third end root equals fraction numerator 1 over denominator square root of 3 end fraction equals fraction numerator 1 over denominator square root of 3 end fraction times fraction numerator square root of 3 over denominator square root of 3 end fraction equals 1 third square root of 3 end style$

Jadi, jawaban yang tepat adalah E.