Pertanyaan

x → 3 lim x 4 − 2 x 3 + 3 x 2 x 3 − x 2 = … ?

$x \to 3 lim \frac{x ^{3} - x ^{2}}{x ^{4} - 2 x ^{3} + 3 x ^{2}} = \dots ?$

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P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Pembahasan

Maka, nilai limit tersebut adalah

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x cubed minus x squared over denominator x to the power of 4 minus 2 x cubed plus 3 x squared end fraction end cell equals cell fraction numerator open parentheses 3 close parentheses cubed minus open parentheses 3 close parentheses squared over denominator open parentheses 3 close parentheses to the power of 4 minus 2 open parentheses 3 close parentheses cubed plus 3 open parentheses 3 close parentheses squared end fraction end cell row blank equals cell fraction numerator 27 minus 9 over denominator 81 minus 2 open parentheses 27 close parentheses plus 3 open parentheses 9 close parentheses end fraction end cell row blank equals cell fraction numerator 18 over denominator 81 minus 54 plus 27 end fraction end cell row blank equals cell 18 over 54 end cell row blank equals cell 1 third end cell end table$

Maka, nilai limit tersebut adalah 1 third.