Roboguru
SD
SMP
SMA
UTBK/SNBT

Iklan

Pertanyaan

x → ∞ lim ​ 3 x − 6 − 16 x 2 + 5 x − 20 ​ = ...

 

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

01

:

02

:

39

:

02

Klaim

Iklan

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 16 x squared plus 5 x minus 20 end root end cell end table adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank infinity end table.

Pembahasan

Pembahasan
lock

Cara 1: Ingat! Pada limit tak hinga bentuk berlaku: Jika maka hasinya jika maka hasinya Jika maka hasinya Maka: Cara 2: Jadi, nilai dari adalah .

Cara 1:

Ingat!

Pada limit tak hinga bentuk limit as x rightwards arrow infinity of 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 berlaku:

  • Jika a greater than p maka hasinya infinity 
  • jika a equals p maka hasinya fraction numerator b minus q over denominator 2 square root of a end fraction
  • Jika a less than p maka hasinya negative infinity  

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of 3 x minus 6 minus square root of 16 x squared plus 5 x minus 20 end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of left parenthesis 3 x minus 6 right parenthesis squared end root minus square root of 16 x squared plus 5 x minus 20 end root end cell row blank equals cell square root of 9 x squared minus 36 x plus 36 end root minus square root of 16 x squared plus 5 x minus 20 end root end cell end table 

 karena space 9 less than 16 comma space maka colon 

   table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 16 x squared plus 5 x minus 20 end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank infinity end table 

 

Cara 2:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of 3 x minus 6 minus square root of 16 x squared plus 5 x minus 20 end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of left parenthesis 3 x minus 6 right parenthesis squared end root minus square root of 16 x squared plus 5 x minus 20 end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of 9 x squared minus 36 x plus 36 end root minus square root of 16 x squared plus 5 x minus 20 end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of 9 x squared minus 36 x plus 36 end root minus square root of 16 x squared plus 5 x minus 20 end root cross times fraction numerator square root of 9 x squared minus 36 x plus 36 end root plus square root of 16 x squared plus 5 x minus 20 end root over denominator square root of 9 x squared minus 36 x plus 36 end root plus square root of 16 x squared plus 5 x minus 20 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator left parenthesis 9 x squared minus 36 x plus 36 right parenthesis minus left parenthesis 16 x squared plus 5 x minus 20 right parenthesis over denominator square root of 9 x squared minus 36 x plus 36 end root plus square root of 16 x squared plus 5 x minus 20 end root end fraction end cell row space equals cell limit as x rightwards arrow infinity of fraction numerator negative 7 x squared minus 41 x plus 56 over denominator square root of 9 x squared minus 36 x plus 36 end root plus square root of 16 x squared plus 5 x minus 20 end root end fraction end cell row space equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator negative 7 x squared over denominator x squared end fraction end style minus begin display style fraction numerator 41 x over denominator x squared end fraction end style plus begin display style 56 over x squared end style over denominator square root of begin display style fraction numerator 9 x squared over denominator x to the power of 4 end fraction end style minus begin display style fraction numerator 36 x over denominator x to the power of 4 end fraction end style plus begin display style 36 over x to the power of 4 end style end root plus square root of begin display style fraction numerator 16 x squared over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 5 x over denominator x to the power of 4 end fraction end style minus begin display style 20 over x to the power of 4 end style end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style negative 7 minus 41 over x plus 56 over x squared end style over denominator square root of begin display style 9 over x squared minus 36 over x cubed plus 36 over x to the power of 4 end style end root plus square root of begin display style 16 over x squared plus 5 over x cubed minus 20 over x to the power of 4 end style end root end fraction end cell row blank equals cell fraction numerator begin display style negative 7 minus 0 plus 0 end style over denominator square root of begin display style 0 minus 0 plus 0 end style end root plus square root of begin display style 0 plus 0 minus 0 end style end root end fraction end cell row blank equals cell fraction numerator negative 7 over denominator 0 end fraction end cell row blank equals cell negative infinity end cell end table

 

Jadi, nilai dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 16 x squared plus 5 x minus 20 end root end cell end table adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank infinity end table.

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

1

Iklan

Gold Icon

Klaim Gold gratis sekarang!

Dengan Gold kamu bisa tanya soal ke Forum sepuasnya, lho.

Pertanyaan serupa

Nilai dari L i m x → ∞ ​ ( 7 x − 3 ​ − 7 x + 1 ​ ) =

3

4.2

Jawaban terverifikasi

Error converting from MathML to accessible text.

1

4.3

Jawaban terverifikasi

Iklan

Nilai dari x → ∞ lim ​ ( 4 x 2 − 8 x + 6 ​ − 4 x 2 + 16 x − 3 ​ ) = .....

1

4.8

Jawaban terverifikasi

Nilai dari x → ∞ lim ​ ( 81 x 2 − 10 x + 15 ​ − 9 x + 1 ) = ....

1

4.5

Jawaban terverifikasi

Nilai dari x → ∞ lim ​ x + x + x ​ ​ ​ x ​ ​ = ...

1

4.2

Jawaban terverifikasi
Ruangguru

RUANGGURU HQ

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

Coba GRATIS Aplikasi Roboguru

Download di Google Play

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Bantuan & Panduan

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

[email protected]

Contact 02130930000

02130930000

Ikuti Kami

©2026 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia