Nilai dari x→0lim​x2−3xx2+2x​ adalah ...

Pertanyaan

Nilai dari limit as x rightwards arrow 0 of fraction numerator x squared plus 2 x over denominator x squared minus 3 x end fraction adalah ...

  1. 1 third 

  2. 2 over 3 

  3. 3 over 2 

  4. negative 2 over 3 

  5. negative 3 over 2 

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Diketahui limit as x rightwards arrow 0 of fraction numerator x squared plus 2 x over denominator x squared minus 3 x end fraction.

Gunakan metode substitusi langsung.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator x squared plus 2 x over denominator x squared minus 3 x end fraction end cell equals cell fraction numerator 0 squared plus 2 times 0 over denominator 0 squared minus 3 times 0 end fraction end cell row blank equals cell 0 over 0 space open parentheses tak space tentu close parentheses end cell end table 

Karena hasilnya tak tentu, maka gunakan metode lain.

Fungsi pada limit merupakan fungsi kuadrat, maka gunakan metode pemfaktoran untuk menentukan nilai limit.

Nilai dari limit as x rightwards arrow 0 of fraction numerator x squared plus 2 x over denominator x squared minus 3 x end fraction adalah:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of fraction numerator x squared plus 2 x over denominator x squared minus 3 x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x open parentheses x plus 2 close parentheses over denominator x open parentheses x minus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x plus 2 over denominator x minus 3 end fraction end cell row blank equals cell fraction numerator 0 plus 2 over denominator 0 minus 3 end fraction end cell row blank equals cell negative 2 over 3 end cell end table 

Sehingga, 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 squared plus 2 x over denominator x squared minus 3 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 2 over 3 end cell end table.

Jadi, jawaban yang tepat adalah D.

95

5.0 (5 rating)

Asvira Syahraini AR.

Ini yang aku cari!

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