Roboguru

Tentukan nilai limit fungsi berikut! b. dengan memisalkan

Pertanyaan

Tentukan nilai limit fungsi berikut!

b. begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator square root of x plus 1 end root minus 2 over denominator x minus 3 end fraction end style dengan memisalkan begin mathsize 14px style x equals t squared minus 1 end style

Pembahasan Soal:

Dengan memisalkan begin mathsize 14px style x equals t squared end style maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator square root of x plus 1 end root minus 2 over denominator x minus 3 end fraction end cell equals cell limit as t squared minus 1 rightwards arrow 1 of fraction numerator square root of t squared minus 1 plus 1 end root minus 2 over denominator open parentheses t squared minus 1 close parentheses minus 3 end fraction end cell row blank equals cell limit as t squared minus 1 rightwards arrow 1 of fraction numerator t minus 2 over denominator t squared minus 4 end fraction end cell row blank equals cell limit as t squared minus 1 rightwards arrow 1 of fraction numerator t minus 2 over denominator t squared minus 4 end fraction end cell row blank equals cell limit as t squared minus 1 rightwards arrow 1 of fraction numerator t minus 2 over denominator open parentheses t minus 2 close parentheses space open parentheses t plus 2 close parentheses end fraction end cell row blank equals cell limit as t squared minus 1 rightwards arrow 1 of 1 over blank end cell row blank equals cell limit as t rightwards arrow square root of 2 of fraction numerator 1 over denominator open parentheses t plus 2 close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 2 plus 2 end fraction end cell end table end style

Jadi,nilai limit begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of x plus 1 end root minus 2 over denominator x minus 3 end fraction end cell end table end style  adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator size 14px 1 over denominator square root of size 14px 2 size 14px plus size 14px 2 end fraction end cell end table 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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

Ikuti Kami

©2021 Ruangguru. All Rights Reserved