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Pertanyaan

Tentukan nilai dari limit berikut:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell lim subscript x rightwards arrow infinity end subscript fraction numerator 4 straight x cubed plus 2 straight x plus 1 over denominator 5 straight x cubed plus 8 straight x squared plus 6 end fraction end cell end table

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari table attributes columnalign right center left columnspacing 0px end attributes row cell lim subscript x rightwards arrow infinity end subscript fraction numerator 4 straight x cubed plus 2 straight x plus 1 over denominator 5 straight x cubed plus 8 straight x squared plus 6 end fraction end cell equals cell 4 over 5 end cell end table.

Pembahasan

Ingat bahwa, pada limit tak hingga apabila pangkat tertinggi pembilang sama dengan pangkat tertinggi penyebut, maka hasil limitnya adalah perbandingan koefisien pangkat tertinggi pembilang dan penyebut.

table attributes columnalign right center left columnspacing 0px end attributes row cell lim subscript x rightwards arrow infinity end subscript fraction numerator 4 straight x cubed plus 2 straight x plus 1 over denominator 5 straight x cubed plus 8 straight x squared plus 6 end fraction end cell equals cell lim subscript x rightwards arrow infinity end subscript fraction numerator begin display style 4 straight x cubed plus 2 straight x plus 1 end style over denominator begin display style 5 straight x cubed plus 8 straight x squared plus 6 end style end fraction. fraction numerator begin display style 1 over x cubed end style over denominator begin display style 1 over x cubed end style end fraction end cell row blank equals cell lim subscript x rightwards arrow infinity end subscript fraction numerator 4 plus begin display style 2 over x squared end style plus begin display style 1 over x cubed end style over denominator 5 plus begin display style 8 over x end style plus begin display style 6 over x cubed end style end fraction end cell row blank equals cell fraction numerator 4 plus 0 plus 0 over denominator 5 plus 0 plus 0 end fraction end cell row blank equals cell 4 over 5 end cell end table

Jadi, nilai dari table attributes columnalign right center left columnspacing 0px end attributes row cell lim subscript x rightwards arrow infinity end subscript fraction numerator 4 straight x cubed plus 2 straight x plus 1 over denominator 5 straight x cubed plus 8 straight x squared plus 6 end fraction end cell equals cell 4 over 5 end cell end table.

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