Pertanyaan

Tentukan nilai limit berikut. c.

Tentukan nilai limit berikut.

c. $size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below size 14px space fraction numerator size 14px x to the power of size 14px 4 size 14px minus size 14px 3 size 14px x to the power of size 14px 3 size 14px plus size 14px 2 size 14px x to the power of size 14px 2 over denominator size 14px x to the power of size 14px 3 size 14px minus size 14px 8 end fraction$

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of space fraction numerator x to the power of 4 minus 3 x cubed plus 2 x squared over denominator x cubed minus 8 end fraction end cell equals cell limit as x rightwards arrow 2 of space fraction numerator x squared left parenthesis x squared minus 3 x plus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis left parenthesis x squared plus 2 x plus 4 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of space fraction numerator x squared left parenthesis x minus 2 right parenthesis left parenthesis x minus 1 right parenthesis over denominator left parenthesis x minus 2 right parenthesis left parenthesis x squared plus 2 x plus 4 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of space fraction numerator x squared left parenthesis x minus 1 right parenthesis over denominator x squared plus 2 x plus 4 end fraction end cell row blank equals cell fraction numerator 2 squared left parenthesis 2 minus 1 right parenthesis over denominator 2 squared plus 2 left parenthesis 2 right parenthesis plus 4 end fraction end cell row blank equals cell 4 over 12 end cell row blank equals cell 1 third end cell end table end style$