Iklan

Iklan

Pertanyaan

x → ∞ lim ​ ( x 2 − 5 x ​ − x − 2 ) = ...

 

Iklan

N. Puspita

Master Teacher

Jawaban terverifikasi

Iklan

Pembahasan

Pembahasan
lock

Diperhatikan limit bentuk tak tentu berikut. jika dan hanya jika jika dan hanya jika jika dan hanya jika Sehingga dengan .

Diperhatikan limit bentuk tak tentu begin mathsize 14px style infinity minus infinity end style berikut.

begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root close parentheses equals L end style 

  • begin mathsize 14px style L equals negative infinity end style jika dan hanya jika begin mathsize 14px style a less than p end style
  • L equals fraction numerator b minus q over denominator 2 square root of a end fraction jika dan hanya jika begin mathsize 14px style a equals p end style
  • begin mathsize 14px style L equals infinity end style jika dan hanya jika begin mathsize 14px style a greater than p end style

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses square root of x squared minus 5 x end root minus x minus 2 close parentheses end cell equals cell limit as x rightwards arrow infinity of open parentheses square root of x squared minus 5 x end root minus left parenthesis x plus 2 right parenthesis close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of x squared minus 5 x end root minus square root of left parenthesis x plus 2 right parenthesis squared end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of x squared minus 5 x end root minus square root of x squared plus 4 x plus 4 end root close parentheses end cell row blank equals L end table end style 

 dengan 

begin mathsize 14px style L equals fraction numerator negative 5 minus 4 over denominator 2 square root of 1 end fraction equals fraction numerator negative 9 over denominator 2 end fraction end style.

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

5

Sendi Muladi

Pembahasan lengkap banget Ini yang aku cari! Mudah dimengerti Bantu banget Makasih ❤️

gayatri zakiyyah

Mudah dimengerti

Iklan

Iklan

Pertanyaan serupa

x → ∞ lim ​ ( x + 1 ​ − x ​ ) = ....

9

4.5

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

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

[email protected]

Contact 02140008000

02140008000

Ikuti Kami

©2024 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia