Pertanyaan

Nilai x → 1 lim x 3 − 1 x 2 − 5 x + 4 = ...

Nilai $x \to 1 lim \frac{x ^{2} - 5 x + 4}{x ^{3} - 1} = ...$

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R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai

nilai $limit as x rightwards arrow 1 of fraction numerator x squared minus 5 x plus 4 over denominator x cubed minus 1 end fraction equals negative 1.$

Pembahasan

Nilai dapat ditentukan dengan mensubstitusi nilai ke dalam fungsi sehingga Karena hasil menggunakan konsep limit yaitu cara substitusi adalah maka untuk menentukan limitnya menggunakan cara selanjutnya yaitu pemfaktoran sebagai berikut Jadi nilai

Nilai $limit as x rightwards arrow 1 of fraction numerator x squared minus 5 x plus 4 over denominator x cubed minus 1 end fraction$ dapat ditentukan dengan mensubstitusi nilai x equals 1 ke dalam fungsi $fraction numerator x squared minus 5 x plus 4 over denominator x cubed minus 1 end fraction$ sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator x squared minus 5 x plus 4 over denominator x cubed minus 1 end fraction end cell equals cell fraction numerator open parentheses 1 close parentheses squared minus 5 open parentheses 1 close parentheses plus 4 over denominator open parentheses 1 close parentheses cubed minus 1 end fraction end cell row cell limit as x rightwards arrow 1 of fraction numerator x squared minus 5 x plus 4 over denominator x cubed minus 1 end fraction end cell equals cell fraction numerator 1 minus 5 plus 4 over denominator 1 minus 1 end fraction end cell row cell limit as x rightwards arrow 1 of fraction numerator x squared minus 5 x plus 4 over denominator x cubed minus 1 end fraction end cell equals cell 0 over 0 end cell end table$

Karena hasil $limit as x rightwards arrow 1 of fraction numerator x squared minus 5 x plus 4 over denominator x cubed minus 1 end fraction$ menggunakan konsep limit yaitu cara substitusi adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 0 over 0 comma end cell end table maka untuk menentukan limitnya menggunakan cara selanjutnya yaitu pemfaktoran sebagai berikut

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator x squared minus 5 x plus 4 over denominator x cubed minus 1 end fraction end cell equals cell limit as x rightwards arrow 1 of fraction numerator up diagonal strike open parentheses x minus 1 close parentheses end strike open parentheses x minus 4 close parentheses over denominator up diagonal strike open parentheses x minus 1 close parentheses end strike open parentheses x squared plus x plus 1 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator x minus 4 over denominator x squared plus x plus 1 end fraction end cell row blank equals cell fraction numerator 1 minus 4 over denominator open parentheses 1 close parentheses squared plus 1 plus 1 end fraction end cell row blank equals cell fraction numerator negative 3 over denominator 3 end fraction end cell row blank equals cell negative 1 end cell end table$

Jadi nilai $limit as x rightwards arrow 1 of fraction numerator x squared minus 5 x plus 4 over denominator x cubed minus 1 end fraction equals negative 1.$