Pertanyaan

Tentukan nilai x → 2 lim x 2 − 5 x + 6 x 2 + 5 x − 14 = ...

Tentukan nilai $x \to 2 lim \frac{x ^{2} + 5 x - 14}{x ^{2} - 5 x + 6} = ...$

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Klaim

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Dengan memfaktorkan persamaan kuadrat yang terdapat pada limit, diperoleh: Jadi,

Dengan memfaktorkan persamaan kuadrat yang terdapat pada limit, diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator x squared plus 5 x minus 14 over denominator x squared minus 5 x plus 6 end fraction end cell equals cell limit as x rightwards arrow 2 of fraction numerator left parenthesis x plus 7 right parenthesis left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 3 right parenthesis left parenthesis x minus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator left parenthesis x plus 7 right parenthesis over denominator left parenthesis x minus 3 right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis 2 plus 7 right parenthesis over denominator left parenthesis 2 minus 3 right parenthesis end fraction end cell row blank equals cell fraction numerator 9 over denominator negative 1 end fraction end cell row blank equals cell negative 9 end cell end table$

Jadi,

$limit as x rightwards arrow 2 of fraction numerator x squared plus 5 x minus 14 over denominator x squared minus 5 x plus 6 end fraction equals negative 9$