Roboguru

Pertanyaan

Tentukan nilai darilimit as x rightwards arrow infinity of fraction numerator x open parentheses 1 minus cos space begin display style 4 over x end style close parentheses over denominator tan space begin display style 1 over x end style end fraction .

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Misalkan 1 over x equals y

Untuk x mendekati infinity maka y mendekati 0.

Bentuk 1 minus cos space 4 y equals 2 space sin squared 2 y 

  table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator x open parentheses 1 minus cos space begin display style 4 over x end style close parentheses over denominator tan space begin display style 1 over x end style end fraction end cell equals cell limit as y rightwards arrow 0 of fraction numerator begin display style 1 over y end style open parentheses 1 minus co s space 4 y close parentheses over denominator tan space y end fraction end cell row blank equals cell limit as y rightwards arrow 0 of fraction numerator begin display style 1 over y end style open parentheses 2 sin squared space 2 y close parentheses over denominator tan space begin display style y end style end fraction end cell row blank equals cell limit as y rightwards arrow 0 of fraction numerator open parentheses 2 space sin squared begin display style space 2 y end style close parentheses over denominator space y space tan begin display style y space end style end fraction end cell row blank equals cell limit as y rightwards arrow 0 of space 2 times fraction numerator sin space 2 y over denominator y end fraction times fraction numerator sin space 2 y over denominator tan space begin display style y end style end fraction end cell row blank equals cell 2 times 2 times 2 end cell row blank equals 8 end table  

Jadi, nilai dari limit as x rightwards arrow infinity of fraction numerator x open parentheses 1 minus cos space begin display style 4 over x end style close parentheses over denominator tan space begin display style 1 over x end style end fraction adalah 8

 

62

0.0 (0 rating)

Pertanyaan serupa

Tentukan nilai limit fungsi berikut. a. x→3π​lim​3tan(x)sin(x)+2cos(x)​

8

0.0

Jawaban terverifikasi

RUANGGURU HQ

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

Coba GRATIS Aplikasi Ruangguru

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