Tentukan nilai dari limit berikut: limx→∞5x3+8x2+64x3+2x+1

Tentukan nilai dari limit berikut: limx→∞5x3+8...

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