Pertanyaan

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

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

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Habis dalam

Klaim

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x cubed plus 2 x squared minus 5 x over denominator x squared plus 2 x end fraction end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 2 end cell end table$ .

Pembahasan

Diketahui . Langkah pertama, gunakan metode substitusi langsung. Karena diperoleh hasil tak tentu dan fungsi pada limit merupakan fungsi kuadrat, maka gunakan metode pemfaktoran. Jadi, .

Diketahui $limit as x rightwards arrow 0 of fraction numerator x cubed plus 2 x squared minus 5 x over denominator x squared plus 2 x end fraction$ .

Langkah pertama, gunakan metode substitusi langsung.

Karena diperoleh hasil tak tentu dan fungsi pada limit merupakan fungsi kuadrat, maka gunakan metode pemfaktoran.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of fraction numerator x cubed plus 2 x squared minus 5 x over denominator x squared plus 2 x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x open parentheses x squared plus 2 x minus 5 close parentheses over denominator x open parentheses x plus 2 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x squared plus 2 x minus 5 over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator 0 squared plus 2 times 0 minus 5 over denominator 0 plus 2 end fraction end cell row blank equals cell negative 5 over 2 end cell end table$

Jadi, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x cubed plus 2 x squared minus 5 x over denominator x squared plus 2 x end fraction end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 2 end cell end table$ .