Pertanyaan

Tentukan nilai limit berikut menggunakan cara pemfaktoran x → 4 lim x − 4 x − 2

Tentukan nilai limit berikut menggunakan cara pemfaktoran

$x \to 4 lim \frac{x - 2}{x - 4}$

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

.

$begin mathsize 14px style limit as x rightwards arrow 4 of fraction numerator square root of x minus 2 over denominator x minus 4 end fraction equals 1 fourth end style$ .

Pembahasan

Dengan terlebih dahulu melakukan pemfaktoran diperoleh Jadi .

$begin mathsize 14px style limit as x rightwards arrow 4 of fraction numerator square root of x minus 2 over denominator x minus 4 end fraction end style$

Dengan terlebih dahulu melakukan pemfaktoran diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of fraction numerator square root of x minus 2 over denominator x minus 4 end fraction end cell equals cell limit as x rightwards arrow 4 of fraction numerator square root of x minus 2 over denominator open parentheses square root of x minus 2 close parentheses open parentheses square root of x plus 2 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator 1 over denominator open parentheses square root of x plus 2 close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 4 plus 2 end fraction end cell row blank equals cell fraction numerator 1 over denominator 2 plus 2 end fraction end cell row blank equals cell 1 fourth end cell end table end style$

Jadi $begin mathsize 14px style limit as x rightwards arrow 4 of fraction numerator square root of x minus 2 over denominator x minus 4 end fraction equals 1 fourth end style$ .