Jika f(x)=x2+x maka h→0lim hf(x+2h)−f(x)=...

Pertanyaan

Jika $\mathrm f\left(\mathrm x\right)=\mathrm x^2+\mathrm x$ maka $limit as straight h rightwards arrow 0 of space fraction numerator straight f open parentheses straight x plus 2 straight h close parentheses minus straight f open parentheses straight x close parentheses over denominator straight h end fraction equals...$

2x
4x
x
2x+2
4x+4

H. Firmansyah

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B

Pembahasan

Diketahui $\mathrm f\left(\mathrm x\right)=\mathrm x^2+\mathrm x$ , akan dicari $limit as straight h rightwards arrow 0 of space fraction numerator straight f open parentheses straight x plus 2 straight h close parentheses minus straight f open parentheses straight x close parentheses over denominator straight h end fraction$

Perhatikan perhitungan berikut

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight h rightwards arrow 0 of space fraction numerator straight f open parentheses straight x plus 2 straight h close parentheses minus straight f open parentheses straight x close parentheses over denominator straight h end fraction end cell equals cell limit as straight h rightwards arrow 0 of space fraction numerator open parentheses straight x plus 2 straight h close parentheses squared plus 2 minus open parentheses straight x squared plus 2 close parentheses over denominator straight h end fraction end cell row blank equals cell limit as straight h rightwards arrow 0 of fraction numerator straight x squared plus 4 hx plus 4 straight h squared plus 2 minus straight x squared minus 2 over denominator straight h end fraction end cell row blank equals cell limit as straight h rightwards arrow 0 of space fraction numerator 4 hx plus 4 straight h squared over denominator straight h end fraction end cell row blank equals cell limit as straight h rightwards arrow 0 of space 4 straight x plus straight h end cell row blank equals cell 4 straight x plus 0 end cell row blank equals cell 4 straight x end cell end table$

Dengan demikian, diperoleh $table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight h rightwards arrow 0 of space fraction numerator straight f open parentheses straight x plus 2 straight h close parentheses minus straight f open parentheses straight x close parentheses over denominator straight h end fraction end cell equals cell 4 straight x end cell end table$

Oleh karena itu, jawaban yang tepat adalah B

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