Pertanyaan

x → 0 lim 2 x − x 2 5 x + x 2 − 2 x 3 = …

$x \to 0 lim \frac{5 x + x ^{2} - 2 x ^{3}}{2 x - x ^{2}} = \dots$

J. Joko

Master Teacher

Jawaban terverifikasi

Jawaban

nilai .

nilai $begin mathsize 14px style limit as x rightwards arrow 0 of invisible function application fraction numerator 5 x plus x squared minus 2 x cubed over denominator 2 x minus x squared end fraction equals 2 1 half end style$ .

Pembahasan

Untuk maka . Diperoleh nilai . Oleh karena itu, harus difaktorkan terlebih dahulu, Jadi nilai .

Untuk maka

$begin mathsize 14px style limit as x rightwards arrow 0 of invisible function application fraction numerator 5 x plus x squared minus 2 x cubed over denominator 2 x minus x squared end fraction equals fraction numerator 5 left parenthesis 0 right parenthesis plus 0 squared minus 2 left parenthesis 0 right parenthesis cubed over denominator 2 left parenthesis 0 right parenthesis minus 0 squared end fraction equals 0 over 0 end style$ .

Diperoleh nilai . Oleh karena itu, harus difaktorkan terlebih dahulu,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of invisible function application fraction numerator 5 x plus x squared minus 2 x cubed over denominator 2 x minus x squared end fraction end cell equals cell limit as x rightwards arrow 0 of invisible function application fraction numerator up diagonal strike x open parentheses 5 plus x minus 2 x squared close parentheses over denominator up diagonal strike x left parenthesis 2 minus x right parenthesis end fraction end cell row blank equals cell fraction numerator 5 plus 0 minus 0 squared over denominator 2 minus 0 end fraction end cell row blank equals cell 5 over 2 end cell row blank equals cell 2 1 half end cell end table end style$

Jadi nilai $begin mathsize 14px style limit as x rightwards arrow 0 of invisible function application fraction numerator 5 x plus x squared minus 2 x cubed over denominator 2 x minus x squared end fraction equals 2 1 half end style$ .