Tentukan nilai limit berikut. b)  x→∞lim​ x1+4x2​−1+9x2​​

Pertanyaan

Tentukan nilai limit berikut.

b)  limit as x rightwards arrow infinity of space fraction numerator square root of 1 plus 4 x squared end root minus square root of 1 plus 9 x squared end root over denominator x end fraction

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

 limit as x rightwards arrow infinity of space fraction numerator square root of 1 plus 4 x squared end root minus square root of 1 plus 9 x squared end root over denominator x end fraction equals negative 1.

Pembahasan

Perhatikan perhitungan berikut ini!

dengan substitusi langsung:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator square root of 1 plus 4 x squared end root minus square root of 1 plus 9 x squared end root over denominator x end fraction end cell equals cell infinity minus infinity space open parentheses tak space tentu close parentheses end cell end table

karena dengan metode substitusi hasilnya tak tentu, maka dapat dikerjakan dengan cara membagi dengan variabel berpangkat tertinggi:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator square root of 1 plus 4 x squared end root minus square root of 1 plus 9 x squared end root over denominator x end fraction end cell equals cell limit as x rightwards arrow infinity of space fraction numerator square root of 1 plus 4 x squared end root minus square root of 1 plus 9 x squared end root over denominator x end fraction times fraction numerator begin display style 1 over x end style over denominator begin display style 1 over x end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator square root of 1 plus 4 x squared end root minus square root of 1 plus 9 x squared end root over denominator square root of x squared end root end fraction end style over denominator begin display style fraction numerator x over denominator square root of x squared end root end fraction end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator square root of 1 over x squared plus fraction numerator 4 x squared over denominator x squared end fraction end root minus square root of 1 over x squared plus fraction numerator 9 x squared over denominator x squared end fraction end root over denominator begin display style x over x end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator square root of 1 over x squared plus 4 end root minus square root of 1 over x squared plus 9 end root over denominator 1 end fraction end cell row blank equals cell fraction numerator square root of limit as x rightwards arrow infinity of 1 over x squared plus limit as x rightwards arrow infinity of 4 end root minus square root of limit as x rightwards arrow infinity of 1 over x squared plus limit as x rightwards arrow infinity of 9 end root over denominator limit as x rightwards arrow infinity of 1 end fraction end cell row blank equals cell fraction numerator square root of 0 plus 4 end root minus square root of 0 plus 9 end root over denominator 1 end fraction end cell row blank equals cell fraction numerator 2 minus 3 over denominator 1 end fraction end cell row blank equals cell fraction numerator negative 1 over denominator 1 end fraction end cell row blank equals cell negative 1 end cell end table

Dengan demikian, limit as x rightwards arrow infinity of space fraction numerator square root of 1 plus 4 x squared end root minus square root of 1 plus 9 x squared end root over denominator x end fraction equals negative 1.

43

5.0 (1 rating)

Pertanyaan serupa

Nilai dari  x→∞lim​(3x+1)−9x2−9x+2​= ....

83

3.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia