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

Pertanyaan

Diketahui f open parentheses x close parentheses equals x cubed. 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 ....

  1. negative 9 a squared minus 6 a

  2. negative 3 a squared minus 6 a

  3. a squared minus 6 a

  4. 3 a squared minus 6 a

  5. 9 a squared minus 6 a

P. Anggrayni

Master Teacher

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Jawaban

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Pembahasan

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Ingat kembali mengenai konsep limit.

limit as x rightwards arrow a of p open parentheses x close parentheses equals p open parentheses a close parentheses

Pada soal diketahui f open parentheses x close parentheses equals x cubed. Kemudian dicari nilai dari f open parentheses a minus 3 x close parentheses dengan subtistusi a minus 3 x ke f open parentheses x close parentheses equals x cubed dan subtitusi a ke f open parentheses x close parentheses equals x cubed

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 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 9 a squared end cell end table.

Oleh karena itu, tidak ada jawaban yang benar.

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