Nilai dari x→0lim​(x2−2x+1​−x2+3x−4​) adalah ...

Pertanyaan

Nilai dari limit as x rightwards arrow 0 of open parentheses square root of x squared minus 2 x plus 1 end root minus square root of x squared plus 3 x minus 4 end root close parentheses adalah ...begin mathsize 14px style space end style 

  1. negative 3space  

  2. negative 1space 

  3. 0 space 

  4. 1space 

  5. 3space 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

tidak ada jawaban yang tepat.

Pembahasan

Terdapat kesalahan pada soal. Bukan limit as x rightwards arrow 0 of open parentheses square root of x squared minus 2 x plus 1 end root minus square root of x squared plus 3 x minus 4 end root close parentheses, melainkan limit as x rightwards arrow infinity of open parentheses square root of x squared minus 2 x plus 1 end root minus square root of x squared plus 3 x minus 4 end root close parentheses.

Ingat!

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 open curly brackets table attributes columnalign left end attributes row cell infinity comma space untuk space a greater than p end cell row cell table row cell fraction numerator b minus q over denominator 2 square root of a end fraction comma space untuk space a equals p end cell row cell negative infinity comma space untuk space a less than p end cell end table end cell end table close 

Diketahui limit as x rightwards arrow infinity of open parentheses square root of x squared minus 2 x plus 1 end root minus square root of x squared plus 3 x minus 4 end root close parentheses, maka:

table attributes columnalign right center left columnspacing 0px end attributes row a equals cell 1 comma space b equals negative 2 comma space c equals 1 end cell row p equals cell 1 comma space q equals 3 comma space r equals negative 4 end cell end table 

Sehingga, nilai dari limit tersebut adalah:

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

Sehingga, 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 cell open parentheses square root of x squared minus 2 x plus 1 end root minus square root of x squared plus 3 x minus 4 end root close parentheses end cell end table equals 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table.

Jadi, tidak ada jawaban yang tepat.

125

4.0 (6 rating)

Pertanyaan serupa

Error converting from MathML to accessible text.

99

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

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