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x→∞lim​x2−x​2x2+3x​=…

Pertanyaan

limit as x rightwards arrow infinity of fraction numerator 2 x squared plus 3 x over denominator square root of x squared minus x end root end fraction equals horizontal ellipsis 

  1. 0 

  2. 1 half 

  3. 1 

  4. 2 

  5. infinity 

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E

Pembahasan

Untuk menentukan limit bentuk tak hingga dapat dilakukan dengan membaginya dengan pangkat tertinggi sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 2 x squared plus 3 x over denominator square root of x squared minus x end root end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 2 x squared over denominator x squared end fraction end style plus begin display style fraction numerator 3 x over denominator x squared end fraction end style over denominator square root of begin display style x squared over x to the power of 4 end style minus begin display style x over x to the power of 4 end style end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 2 plus begin display style 3 over x end style over denominator square root of begin display style 1 over x squared end style minus begin display style 1 over x cubed end style end root end fraction end cell row blank equals cell fraction numerator 2 plus begin display style 3 over infinity end style over denominator square root of begin display style 1 over infinity end style minus begin display style 1 over infinity end style end root end fraction end cell row blank equals cell fraction numerator 2 plus 0 over denominator square root of 0 minus 0 end root end fraction end cell row blank equals cell 2 over 0 end cell row blank equals infinity end table

Jadi, jawaban yang tepat adalah E

206

5.0 (8 rating)

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