Iklan

Pertanyaan

Tentukan b. x → ∞ lim ​ ( x 2 + x ​ − x 2 − 2 x ​ )

Tentukan 

b.  

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

02

:

07

:

24

:

19

Klaim

Iklan

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

.

 limit as x rightwards arrow infinity of space open parentheses square root of x squared plus x end root minus square root of x squared minus 2 x end root close parentheses equals 3 over 2.

Pembahasan

Pembahasan
lock

Perhatikan Jadi, .

Perhatikan 

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

Jadi, limit as x rightwards arrow infinity of space open parentheses square root of x squared plus x end root minus square root of x squared minus 2 x end root close parentheses equals 3 over 2.

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

1

Iklan

Pertanyaan serupa

x → ∞ lim ​ ( x + 1 ​ − x ​ ) = ....

5

4.6

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

©2025 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia