Pertanyaan

x → 0 lim x ( x − 3 ) 2 − 9

$x \to 0 lim \frac{( x - 3 ) ^{2} - 9}{x}$

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

adalah .

$limit as x rightwards arrow 0 of fraction numerator open parentheses x minus 3 close parentheses squared minus 9 over denominator x end fraction$ adalah negative 6

Pembahasan

Menentukan limit fungsi dengan metode subtitusi, jika ada maka dijabarkan dahulu . Jadi, adalah .

Menentukan limit fungsi dengan metode subtitusi, jika ada left parenthesis straight a minus straight b right parenthesis squared equals straight a to the power of 2 end exponent minus 2 ab plus straight b squared maka dijabarkan dahulu open parentheses x minus 3 close parentheses squared .

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator open parentheses x minus 3 close parentheses squared minus 9 over denominator x end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator x squared minus 6 x plus 9 minus 9 over denominator x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x squared minus 6 x over denominator x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator up diagonal strike x cross times left parenthesis x minus 6 right parenthesis over denominator up diagonal strike x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of x minus 6 end cell row blank equals cell 0 minus 6 end cell row blank equals cell negative 6 end cell end table$

Jadi, $limit as x rightwards arrow 0 of fraction numerator open parentheses x minus 3 close parentheses squared minus 9 over denominator x end fraction$ adalah negative 6 .