Pertanyaan

x → 3 lim x 2 − 9 x 3 − 27 = ... .

$x \to 3 lim \frac{x ^{3} - 27}{x ^{2} - 9} = ...$ .

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

diperoleh nilai .

diperoleh nilai $begin mathsize 14px style limit as x rightwards arrow 3 of space fraction numerator x cubed minus 27 over denominator x squared minus 9 end fraction equals 9 over 2 end style$ .

Pembahasan

Gunakan konsep menentukan nilai limit dengan pemfaktoran. Untuk menentukan nilai limit terlebih dahulu cek nilai limit. Setelah di cek nilai limit diperoleh hasil sehingga limit harus disederhanakan. Perhatikan perhitungan berikut, Jadi, diperoleh nilai .

Gunakan konsep menentukan nilai limit dengan pemfaktoran.

Untuk menentukan nilai limit terlebih dahulu cek nilai limit.

$begin mathsize 14px style limit as x rightwards arrow 3 of space fraction numerator x cubed minus 27 over denominator x squared minus 9 end fraction equals fraction numerator open parentheses 3 close parentheses cubed minus 27 over denominator open parentheses 3 close parentheses squared minus 9 end fraction equals fraction numerator 27 minus 27 over denominator 9 minus 9 end fraction equals 0 over 0 end style$

Setelah di cek nilai limit diperoleh hasil begin mathsize 14px style 0 over 0 end style sehingga limit harus disederhanakan.

Perhatikan perhitungan berikut,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as x rightwards arrow 3 of space fraction numerator x cubed minus 27 over denominator x squared minus 9 end fraction end cell equals cell limit as x rightwards arrow 3 of space fraction numerator up diagonal strike open parentheses x minus 3 close parentheses end strike open parentheses x squared plus 3 x plus 9 close parentheses over denominator up diagonal strike open parentheses x minus 3 close parentheses end strike open parentheses x plus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of space fraction numerator x squared plus 3 x plus 9 over denominator x plus 3 end fraction end cell row blank equals cell fraction numerator open parentheses 3 close parentheses squared plus 3 open parentheses 3 close parentheses plus 9 over denominator open parentheses 3 close parentheses plus 3 end fraction end cell row blank equals cell fraction numerator 9 plus 9 plus 9 over denominator 3 plus 3 end fraction end cell row blank equals cell 27 over 6 end cell row cell limit as x rightwards arrow 3 of space fraction numerator x cubed minus 27 over denominator x squared minus 9 end fraction end cell equals cell 9 over 2 end cell end table end style$

Jadi, diperoleh nilai $begin mathsize 14px style limit as x rightwards arrow 3 of space fraction numerator x cubed minus 27 over denominator x squared minus 9 end fraction equals 9 over 2 end style$ .