Pertanyaan

Hitunglah limit fungsi berikut! d.

Hitunglah limit fungsi berikut!

d. $size 14px lim with size 14px x size 14px rightwards arrow size 14px 0 below fraction numerator size 14px x size 14px minus size 14px x to the power of size 14px 2 over denominator size 14px x size 14px minus size 14px x to the power of size 14px 2 size 14px plus size 14px x to the power of size 14px 3 end fraction$

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai adalah 1.

nilai $size 14px lim with size 14px x size 14px rightwards arrow size 14px 0 below fraction numerator size 14px x size 14px minus size 14px x to the power of size 14px 2 over denominator size 14px x size 14px minus size 14px x to the power of size 14px 2 size 14px plus size 14px x to the power of size 14px 3 end fraction$ adalah 1.

Pembahasan

disubtitusikan pada limit tersebut Karena menghasilkan limit bentuk tak tentumaka akan ditentukan dengan metode pemfaktoran Jadi, nilai adalah 1.

disubtitusikan pada limit tersebut

$begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x minus x squared over denominator x minus x squared plus x cubed end fraction equals fraction numerator 0 minus 0 over denominator 0 minus 0 plus 0 end fraction equals 0 over 0 end style$

Karena menghasilkan limit bentuk tak tentu maka akan ditentukan dengan metode pemfaktoran

$table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 0 below fraction numerator size 14px x size 14px minus size 14px x to the power of size 14px 2 over denominator size 14px x size 14px minus size 14px x to the power of size 14px 2 size 14px plus size 14px x to the power of size 14px 3 end fraction end cell size 14px equals cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 0 below fraction numerator up diagonal strike size 14px x begin mathsize 14px style left parenthesis 1 minus x right parenthesis end style over denominator up diagonal strike size 14px x begin mathsize 14px style left parenthesis 1 minus x plus x squared right parenthesis end style end fraction end cell row cell size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space end cell size 14px equals cell fraction numerator size 14px 1 size 14px minus size 14px 0 over denominator size 14px 1 size 14px minus size 14px 0 size 14px plus size 14px 0 end fraction end cell row cell size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space end cell size 14px equals size 14px 1 end table$

Jadi, nilai $size 14px lim with size 14px x size 14px rightwards arrow size 14px 0 below fraction numerator size 14px x size 14px minus size 14px x to the power of size 14px 2 over denominator size 14px x size 14px minus size 14px x to the power of size 14px 2 size 14px plus size 14px x to the power of size 14px 3 end fraction$ adalah 1.