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Nilai x→∞lim​(4x2−3x+8​−2x+1)= … +3mu.

Pertanyaan

Nilai limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 3 x plus 8 end root minus 2 x plus 1 close parentheses equals space horizontal ellipsis. 

  1. 1 comma 75 

  2. 0 comma 25 

  3. negative 3 comma 5 

  4. 24 comma 7 

  5. 0 

M. Ulfa

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Untuk menyelesaikan limit tak hingga bentuk akar dapat digunakan rumus

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of square root of a x squared plus b x plus c end root minus square root of a x squared plus p x plus q end root end cell row blank equals cell fraction numerator b minus p over denominator 2 square root of a end fraction end cell end table 

Fungsi pada limit di atas dapat diubah bentuk seperti berikut,

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 3 x plus 8 end root minus 2 x plus 1 close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 3 x plus 8 end root minus square root of left parenthesis 2 x minus 1 right parenthesis squared end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 3 x plus 8 end root minus square root of 4 x squared minus 4 x plus 1 end root close parentheses end cell end table  

Maka didapatkan a equals 4b equals negative 3, dan p equals negative 4.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 3 x plus 8 end root minus 2 x plus 1 close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 3 x plus 8 end root minus square root of 4 x squared minus 4 x plus 1 end root close parentheses end cell row blank equals cell fraction numerator negative 3 minus left parenthesis negative 4 right parenthesis over denominator 2 square root of 4 end fraction end cell row blank equals cell fraction numerator negative 3 plus 4 over denominator 2 times 2 end fraction end cell row blank equals cell 1 fourth end cell row blank equals cell 0 comma 25 end cell end table 

Dengan demikian, hasil dari limit di atas adalah 0 comma 25.

Jadi, jawaban yang tepat adalah B.

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