Tuliskan dan tunjukkan sifat-sifat limit yang mana saja dapat digunakan untuk menyelesaikan limit fungsi berikut x→1limx+4x−4!

Pertanyaan

Tuliskan dan tunjukkan sifat-sifat limit yang mana saja dapat digunakan untuk menyelesaikan limit fungsi berikut $\style{font-size:14px}{\lim_{x\rightarrow1}\frac{x-4}{x+4}}$ !

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Sifat-sifat limit yang digunakan :

1. $begin mathsize 14px style limit as x rightwards arrow a of fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction equals fraction numerator limit as x rightwards arrow a of f left parenthesis x right parenthesis over denominator limit as x rightwards arrow a of g left parenthesis x right parenthesis end fraction end style$

Jadi nilai

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator x minus 4 over denominator x plus 4 end fraction end cell equals cell fraction numerator limit as x rightwards arrow 1 of left parenthesis x minus 4 right parenthesis over denominator limit as x rightwards arrow 1 of left parenthesis x plus 4 right parenthesis end fraction end cell row blank equals cell fraction numerator limit as x rightwards arrow 1 of x minus limit as x rightwards arrow 1 of 4 over denominator limit as x rightwards arrow 1 of x plus limit as x rightwards arrow 1 of 4 end fraction end cell row blank equals cell fraction numerator 1 minus 4 over denominator 1 plus 4 end fraction end cell row blank equals cell negative 3 over 5 end cell end table end style$