Pertanyaan

size 14px lim with size 14px x size 14px rightwards arrow size 14px 3 below fraction numerator size 14px x to the power of size 14px 2 size 14px minus size 14px 5 size 14px x size 14px plus size 14px 6 over denominator size 14px 2 size 14px x size 14px minus size 14px 6 end fraction size 14px equals size 14px. size 14px. size 14px. 

R. Trihandayani

Master Teacher

Jawaban terverifikasi

Jawaban

nilai limit tersebut adalah begin mathsize 14px style 1 half end style.

Pembahasan

Pembahasan

Dengan menggunakan metode substitusi, kita peroleh limit fungsi yang diberikan berbentuk tak tentu begin mathsize 14px style 0 over 0 end style sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x squared minus 5 x plus 6 over denominator 2 x minus 6 end fraction end cell equals cell fraction numerator 3 squared minus 5 times 3 plus 6 over denominator 2 times 3 minus 6 end fraction end cell row blank equals cell 0 over 0 end cell end table end style 

Oleh karena itu, kita menggunakan metode pemfaktoran untuk memperoleh limit fungsi aljabar yang diberikan sebagai berikut.

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 3 below fraction numerator size 14px x to the power of size 14px 2 size 14px minus size 14px 5 size 14px x size 14px plus size 14px 6 over denominator size 14px 2 size 14px x size 14px minus size 14px 6 end fraction end cell size 14px equals cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 3 below fraction numerator size 14px left parenthesis size 14px x size 14px minus size 14px 3 size 14px right parenthesis size 14px left parenthesis size 14px x size 14px minus size 14px 2 size 14px right parenthesis over denominator size 14px 2 size 14px left parenthesis size 14px x size 14px minus size 14px 3 size 14px right parenthesis end fraction end cell row blank size 14px equals cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 3 below fraction numerator size 14px left parenthesis size 14px x size 14px minus size 14px 2 size 14px right parenthesis over denominator size 14px 2 end fraction end cell row blank size 14px equals cell fraction numerator size 14px 3 size 14px minus size 14px 2 over denominator size 14px 2 end fraction end cell row blank size 14px equals cell size 14px 1 over size 14px 2 end cell end table 

Jadi, nilai limit tersebut adalah begin mathsize 14px style 1 half end style.

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