Pertanyaan

Tentukan hasil dari 3 x → 3 lim x − 3 2 x 2 − 4 x − 6

Tentukan hasil dari $3 x \to 3 lim \frac{2 x ^{2} - 4 x - 6}{x - 3}$

J. Joko

Master Teacher

Jawaban terverifikasi

Jawaban

nilai .

nilai $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell cube root of limit as x rightwards arrow 3 of invisible function application fraction numerator 2 x squared minus 4 x minus 6 over denominator x minus 3 end fraction end root end cell end table equals 2 end style$ .

Pembahasan

Untuk maka . Diperoleh nilai . Oleh karena itu, harus difaktorkan terlebih dahulu, Jadi nilai .

Untuk maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell cube root of limit as x rightwards arrow 3 of invisible function application fraction numerator 2 x squared minus 4 x minus 6 over denominator x minus 3 end fraction end root end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell cube root of limit as x rightwards arrow 3 of invisible function application fraction numerator 2 left parenthesis 3 right parenthesis squared minus 4 left parenthesis 3 right parenthesis minus 6 over denominator 3 minus 3 end fraction end root end cell end table equals 0 over 0 end style$ .

Diperoleh nilai . Oleh karena itu, harus difaktorkan terlebih dahulu,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of limit as x rightwards arrow 3 of invisible function application fraction numerator 2 x squared minus 4 x minus 6 over denominator x minus 3 end fraction end root space end cell equals cell cube root of limit as x rightwards arrow 3 of invisible function application fraction numerator 2 open parentheses x squared minus 2 x minus 3 close parentheses over denominator x minus 3 end fraction end root space end cell row blank equals cell cube root of limit as x rightwards arrow 3 of invisible function application fraction numerator 2 up diagonal strike left parenthesis x minus 3 right parenthesis end strike left parenthesis x plus 1 right parenthesis over denominator up diagonal strike left parenthesis x minus 3 right parenthesis end strike end fraction end root space end cell row blank equals cell cube root of 2 left parenthesis 3 plus 1 right parenthesis end root end cell row blank equals cell cube root of 8 end cell row blank equals cell 2 space end cell end table end style$

Jadi nilai $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell cube root of limit as x rightwards arrow 3 of invisible function application fraction numerator 2 x squared minus 4 x minus 6 over denominator x minus 3 end fraction end root end cell end table equals 2 end style$ .