Pertanyaan

Nilai dari x → 4 lim 1 − x − 3 x 2 − 16 = ....

Nilai dari $x \to 4 lim \frac{x ^{2} - 16}{1 - x - 3}$ = ....

N. Sari

Master Teacher

Mahasiswa/Alumni Universitas Nasional

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D

Pembahasan

Dengan menggunakan sifat penyelesaian limit dengan perkalian sekawan, maka didapatkan : Maka, nilai dari adalah Oleh karena itu, jawaban yang benar adalah D

Dengan menggunakan sifat penyelesaian limit dengan perkalian sekawan, maka didapatkan :

$limit as x rightwards arrow 4 of fraction numerator x squared minus 16 over denominator 1 minus square root of x minus 3 end root end fraction cross times fraction numerator 1 plus square root of x minus 3 end root over denominator 1 plus square root of x minus 3 end root end fractionequals limit as x rightwards arrow 4 of fraction numerator open parentheses x squared minus 16 close parentheses cross times open parentheses 1 plus square root of x minus 3 end root close parentheses over denominator 1 squared minus open parentheses square root of x minus 3 end root close parentheses squared end fractionequals limit as x rightwards arrow 4 of fraction numerator open parentheses x squared minus 16 close parentheses cross times open parentheses 1 plus square root of x minus 3 end root close parentheses over denominator 1 minus open parentheses x minus 3 close parentheses end fractionequals limit as x rightwards arrow 4 of fraction numerator open parentheses x minus 4 close parentheses open parentheses x plus 4 close parentheses cross times open parentheses 1 plus square root of x minus 3 end root close parentheses over denominator 1 minus x plus 3 end fractionequals limit as x rightwards arrow 4 of fraction numerator open parentheses x minus 4 close parentheses open parentheses x plus 4 close parentheses cross times open parentheses 1 plus square root of x minus 3 end root close parentheses over denominator 4 minus x end fractionequals limit as x rightwards arrow 4 of fraction numerator up diagonal strike open parentheses x minus 4 close parentheses end strike open parentheses x plus 4 close parentheses cross times open parentheses 1 plus square root of x minus 3 end root close parentheses over denominator negative up diagonal strike left parenthesis x minus 4 right parenthesis end strike end fractionequals limit as x rightwards arrow 4 of open parentheses negative left parenthesis x plus 4 right parenthesis cross times open parentheses 1 plus square root of x minus 3 end root close parentheses close parenthesesequals negative left parenthesis 4 plus 4 right parenthesis cross times open parentheses 1 plus square root of 4 minus 3 end root close parenthesesequals negative 8 cross times 2equals negative 16$

Maka, nilai dari $limit as x rightwards arrow 4 of fraction numerator x squared minus 16 over denominator 1 minus square root of x minus 3 end root end fraction$ adalah negative 16

Oleh karena itu, jawaban yang benar adalah D