Pertanyaan

Nilai lim x → 4 1 − x − 3 x 2 − 16 adalah ....

Nilai $lim_{x \to 4} \frac{x ^{2} - 16}{1 - x - 3}$ adalah ....

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

Jawaban yang benar adalah A

Pembahasan

Dengan menerapkan konsep perkalian sekawan; Jadi, Nilai dari . Oleh karena itu, Jawaban yang benar adalah A

Dengan menerapkan konsep perkalian sekawan;

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow 4 of fraction numerator straight x squared minus 16 over denominator 1 minus square root of straight x minus 3 end root end fraction end cell equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x squared minus 16 right parenthesis over denominator 1 minus square root of straight x minus 3 end root end fraction times fraction numerator left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis over denominator left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x squared minus 16 right parenthesis left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis over denominator left parenthesis 1 squared minus left parenthesis square root of straight x minus 3 end root right parenthesis squared end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x squared minus 16 right parenthesis left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis over denominator 1 minus left parenthesis straight x minus 3 right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x squared minus 16 right parenthesis left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis over denominator 1 minus straight x plus 3 end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x squared minus 16 right parenthesis left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis over denominator 4 minus straight x end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x minus 4 right parenthesis left parenthesis straight x plus 4 right parenthesis left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis over denominator negative left parenthesis straight x minus 4 right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x plus 4 right parenthesis left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis over denominator negative 1 end fraction end cell row blank equals cell fraction numerator left parenthesis 4 plus 4 right parenthesis left parenthesis 1 plus square root of 4 minus 3 end root right parenthesis over denominator negative 1 end fraction end cell row blank equals cell fraction numerator 8 times 2 over denominator negative 1 end fraction end cell row blank equals cell negative 16 end cell end table end style$

Jadi, Nilai dari .

Oleh karena itu, Jawaban yang benar adalah A