RoboguruRoboguru
SD

hitunglah x→∞lim​4x2−5x+1​−4x2−2x+3​

Pertanyaan

hitunglah limit as x rightwards arrow infinity of square root of 4 x squared minus 5 x plus 1 end root minus square root of 4 x squared minus 2 x plus 3 end root

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Untuk limit tak hingga bentuk akar, dapat diselesaiakan dengan rumus:

limit as straight x rightwards arrow infinity of square root of ax squared plus bx plus straight c end root minus square root of px squared plus qx plus straight r end root equals fraction numerator straight b minus straight q over denominator 2 square root of straight a end fraction comma space untuk space straight a equals straight p

sehingga, untuk fungsi limit

limit as x rightwards arrow infinity of square root of 4 x squared minus 5 x plus 1 end root minus square root of 4 x squared minus 2 x plus 3 end root

diketahui:

a equals 4 comma space b equals negative 5 comma space c equals 1 comma space p equals 4 comma space q equals negative 2 space dan space r equals 3, sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of square root of 4 x squared minus 5 x plus 1 end root minus square root of 4 x squared minus 2 x plus 3 end root end cell equals cell fraction numerator negative 5 minus open parentheses negative 2 close parentheses over denominator 2 square root of 4 end fraction end cell row blank equals cell fraction numerator negative 5 plus 2 over denominator 2 cross times 2 end fraction end cell row blank equals cell fraction numerator negative 3 over denominator 4 end fraction end cell end table

Jadi, hasil dari limit as x rightwards arrow infinity of square root of 4 x squared minus 5 x plus 1 end root minus square root of 4 x squared minus 2 x plus 3 end root adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 3 over denominator 4 end fraction end cell end table

 

48

5.0 (2 rating)

Nadzli Fattahul Iskhi

Pembahasan lengkap banget

Pertanyaan serupa

Nilai dari x→∞lim​(x(4x+5)​−4x2−3​) adalah ...

92

1.0

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