Roboguru

Nilai

Pertanyaan

Nilai limit as x rightwards arrow infinity of open parentheses fraction numerator 3 x to the power of 4 plus x cubed minus 5 over denominator 2 cubed plus x squared minus 5 x plus 10 end fraction close parentheses equals... 

  1. negative 3 over 2

  2. 3 over 2

  3. 1

  4. 0

Pembahasan Soal:

Ingatlah rumus cepat untuk menghitung limit tak hingga.

limit as x rightwards arrow infinity of equals fraction numerator a x to the power of m plus b x to the power of m minus 1 end exponent plus c x to the power of m minus 2 end exponent plus... over denominator p x to the power of n plus q x to the power of n minus 1 end exponent plus r x to the power of n minus 2 end exponent plus... end fraction equals open curly brackets table attributes columnalign left end attributes row cell 0 comma space untuk space m less than n end cell row cell a over p comma space untuk space m equals n infinity comma space untuk space m greater than n end cell end table close

Pertama-tama, gunakan metode substitusi untuk mencari limit pada soal

limit as x rightwards arrow infinity of open parentheses fraction numerator 3 x to the power of 4 plus x cubed minus 5 over denominator 2 cubed plus x squared minus 5 x plus 10 end fraction close parentheses equals infinity over infinity

Limit menghasilkan bentuk tak tentu, maka gunakan rumus cepat limit tak hingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses fraction numerator 3 x to the power of 4 plus x cubed minus 5 over denominator 2 cubed plus x squared minus 5 x plus 10 end fraction close parentheses end cell equals cell limit as x rightwards arrow infinity of open parentheses fraction numerator 3 x to the power of 4 plus x cubed minus 5 over denominator x squared minus 5 x plus 10 plus 2 cubed end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses fraction numerator 3 x to the power of 4 plus x cubed minus 5 over denominator x squared minus 5 x plus 18 end fraction close parentheses space rightwards arrow space pangkat space 4 greater than 2 end cell row blank equals infinity end table

Dengan demikian, hasil dari limit di atas adalah infinity.

Oleh karena itu, tidak ada jawaban yang benar.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Juli 2021

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