Pertanyaan

Hitunglah limit fungsi berikut! d. x → 5 lim x 2 − 4 x − 5 x 2 − 25

Hitunglah limit fungsi berikut!

d. $x \to 5 lim \frac{x ^{2} - 25}{x ^{2} - 4 x - 5}$

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai adalah .

nilai $begin mathsize 14px style limit as x rightwards arrow 5 of fraction numerator x squared minus 25 over denominator x squared minus 4 x minus 5 end fraction end style$ adalah

Pembahasan

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

disubtitusikan pada limit tersebut

$begin mathsize 14px style limit as x rightwards arrow 5 of fraction numerator x squared minus 25 over denominator x squared minus 4 x minus 5 end fraction equals fraction numerator 5 squared minus 25 over denominator 5 squared minus 4 open parentheses 5 close parentheses minus 5 end fraction equals 0 over 0 end style$

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

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 5 of fraction numerator x squared minus 25 over denominator x squared minus 4 x minus 5 end fraction end cell equals cell limit as x rightwards arrow 5 of fraction numerator up diagonal strike open parentheses x minus 5 close parentheses end strike open parentheses x plus 5 close parentheses over denominator up diagonal strike open parentheses x minus 5 close parentheses end strike open parentheses x plus 1 close parentheses end fraction end cell row cell space space space space space space space space space space space space space space space space space space space space space space end cell equals cell fraction numerator 5 plus 5 over denominator 5 plus 1 end fraction end cell row cell space space space space space space space space space space space space space space space space space space space space space space end cell equals cell 10 over 6 end cell row cell space space space space space space space space space space space space space space space space space space space space space space end cell equals cell 1 2 over 3 end cell end table end style$

Jadi, nilai $begin mathsize 14px style limit as x rightwards arrow 5 of fraction numerator x squared minus 25 over denominator x squared minus 4 x minus 5 end fraction end style$ adalah .