Pertanyaan

Nilai x → 0 lim 3 x 2 − 5 x 13 x 3 + 14 x 2 − 20 x = ....

Nilai $x \to 0 lim \frac{13 x ^{3} + 14 x ^{2} - 20 x}{3 x ^{2} - 5 x} = ....$

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R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai

nilai $limit as x rightwards arrow 0 of fraction numerator 13 x cubed plus 14 x squared minus 20 x over denominator 3 x squared minus 5 x end fraction equals 4.$

Pembahasan

Karena ketika disubstitusikan nilai bernilai maka cara untuk menentukan nilai limitnya dengan cara pemfaktoran yaitu Jadi nilai

Karena $limit as x rightwards arrow 0 of fraction numerator 13 x cubed plus 14 x squared minus 20 x over denominator 3 x squared minus 5 x end fraction$ ketika disubstitusikan nilai x equals 0 space bernilai 0 over 0 comma maka cara untuk menentukan nilai limitnya dengan cara pemfaktoran yaitu

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator 13 x cubed plus 14 x squared minus 20 x over denominator 3 x squared minus 5 x end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator up diagonal strike x left parenthesis 13 x squared plus 14 x minus 20 right parenthesis over denominator up diagonal strike x left parenthesis 3 x minus 5 right parenthesis end fraction end cell row cell limit as x rightwards arrow 0 of fraction numerator 13 x cubed plus 14 x squared minus 20 x over denominator 3 x squared minus 5 x end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator 13 x squared plus 14 x minus 20 over denominator 3 x minus 5 end fraction end cell row cell limit as x rightwards arrow 0 of fraction numerator 13 x cubed plus 14 x squared minus 20 x over denominator 3 x squared minus 5 x end fraction end cell equals cell fraction numerator 13 open parentheses 0 close parentheses squared plus 14 open parentheses 0 close parentheses minus 20 over denominator 3 open parentheses 0 close parentheses minus 5 end fraction end cell row cell limit as x rightwards arrow 0 of fraction numerator 13 x cubed plus 14 x squared minus 20 x over denominator 3 x squared minus 5 x end fraction end cell equals cell fraction numerator 0 plus 0 minus 20 over denominator 0 minus 5 end fraction end cell row cell limit as x rightwards arrow 0 of fraction numerator 13 x cubed plus 14 x squared minus 20 x over denominator 3 x squared minus 5 x end fraction end cell equals cell fraction numerator negative 20 over denominator negative 5 end fraction end cell row cell limit as x rightwards arrow 0 of fraction numerator 13 x cubed plus 14 x squared minus 20 x over denominator 3 x squared minus 5 x end fraction end cell equals 4 end table$

Jadi nilai $limit as x rightwards arrow 0 of fraction numerator 13 x cubed plus 14 x squared minus 20 x over denominator 3 x squared minus 5 x end fraction equals 4.$