Pertanyaan

Tentukan nilai limit fungsi berikut. 9. x → 4 lim 3 − 2 x + 1 8 − 2 x

Tentukan nilai limit fungsi berikut.

$9. x \to 4 lim \frac{8 - 2 x}{3 - 2 x + 1}$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

nilai dari .

nilai dari $begin mathsize 14px style limit as x rightwards arrow 4 of space fraction numerator 8 minus 2 x over denominator 3 minus square root of 2 x plus 1 end root end fraction equals 6 end style$ .

Pembahasan

Diketahui: Pembagian limit fungsi. Sederhanakan limit fungsi yang diketahui menggunakan metode akar sekawan seperti berikut: Substitusi dengan pada limit fungsi yang telah disederhanakan seperti berikut: Jadi, nilai dari .

Diketahui:

Pembagian limit fungsi.

Sederhanakan limit fungsi yang diketahui menggunakan metode akar sekawan seperti berikut:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of space fraction numerator 8 minus 2 x over denominator 3 minus square root of 2 x plus 1 end root end fraction end cell equals cell limit as x rightwards arrow 4 of space fraction numerator 8 minus 2 x over denominator 3 minus square root of 2 x plus 1 end root end fraction cross times fraction numerator 3 plus square root of 2 x plus 1 end root over denominator 3 plus square root of 2 x plus 1 end root end fraction end cell row blank equals cell limit as x rightwards arrow 4 of space fraction numerator 8 minus 2 x open parentheses 3 plus square root of 2 x plus 1 end root close parentheses over denominator open parentheses 3 minus square root of 2 x plus 1 end root close parentheses open parentheses 3 plus square root of 2 x plus 1 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 4 of space fraction numerator 8 minus 2 x open parentheses 3 plus square root of 2 x plus 1 end root close parentheses over denominator 9 plus 3 square root of 2 x plus 1 end root minus 3 square root of 2 x plus 1 end root minus 2 x minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow 4 of space fraction numerator down diagonal strike 8 minus 2 x end strike open parentheses 3 plus square root of 2 x plus 1 end root close parentheses over denominator down diagonal strike 8 minus 2 x end strike end fraction end cell row blank equals cell limit as x rightwards arrow 4 of space 3 plus square root of 2 x plus 1 end root end cell end table end style$

Substitusi begin mathsize 14px style x end style dengan begin mathsize 14px style 4 end style pada limit fungsi yang telah disederhanakan seperti berikut:

Jadi, nilai dari $begin mathsize 14px style limit as x rightwards arrow 4 of space fraction numerator 8 minus 2 x over denominator 3 minus square root of 2 x plus 1 end root end fraction equals 6 end style$ .