Diketahui f(x)=x3. Nilai dari x→0limxf(a−3x)−f(a) adalah ....

Pertanyaan

Diketahui $f\left(x\right)=x^3$ . Nilai dari $limit as x rightwards arrow 0 of fraction numerator f open parentheses a minus 3 x close parentheses minus f open parentheses a close parentheses over denominator x end fraction$ adalah ....

$-9a^2-6a$
$-3a^2-6a$
$a^2-6a$
$3a^2-6a$
$9a^2-6a$

P. Anggrayni

Master Teacher

Jawaban terverifikasi

Jawaban

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Ingat kembali mengenai konsep limit.

$\lim_{x\rightarrow a}p\left(x\right)=p\left(a\right)$

Pada soal diketahui $f\left(x\right)=x^3$ . Kemudian dicari nilai dari $f\left(a-3x\right)$ dengan subtistusi $a-3x$ ke $f\left(x\right)=x^3$ dan subtitusi $a$ ke $f\left(x\right)=x^3$ .

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of fraction numerator f open parentheses a minus 3 x close parentheses minus f open parentheses a close parentheses over denominator x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator f open parentheses a minus 3 x close parentheses minus f open parentheses a close parentheses over denominator x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator open parentheses a minus 3 x close parentheses cubed minus open parentheses a close parentheses cubed over denominator x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator open parentheses a squared minus 6 a x plus 9 x squared close parentheses open parentheses a minus 3 x close parentheses minus open parentheses a close parentheses cubed over denominator x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator open parentheses a cubed minus 3 a squared x minus 6 a squared x plus 1 8 a x squared plus 9 a x squared minus 27 x cubed close parentheses minus open parentheses a close parentheses cubed over denominator x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator negative 9 a squared x plus 27 a x squared minus 9 x cubed over denominator x end fraction end cell row blank equals cell stack lim space space with x rightwards arrow 0 below minus 9 a squared plus 27 a x minus 9 x squared end cell row blank equals cell negative 9 a squared end cell end table$

Jadi, nilai dari $limit as x rightwards arrow 0 of fraction numerator f open parentheses a minus 3 x close parentheses minus f open parentheses a close parentheses over denominator x end fraction$ adalah $\begin{array}{rcl}&&{-9a}^2\end{array}$ .

Oleh karena itu, tidak ada jawaban yang benar.