Pertanyaan

Nilai dari x → 0 lim x 2 − 3 x tan x = ... .

Nilai dari $x \to 0 lim \frac{tan x}{x ^{2} - 3 x} = ...$ .

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Habis dalam

Klaim

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Gunakan konsep yang memuat tangen dan gunakan dalil L'Hospital. Perhatikan perhitungan berikut. Jadi, jawaban yang tepat adalah D.

Gunakan konsep yang memuat tangen dan gunakan dalil L'Hospital.

$limit as x rightwards arrow 0 of space fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction equals limit as x rightwards arrow 0 of space fraction numerator f apostrophe open parentheses x close parentheses over denominator g apostrophe open parentheses x close parentheses end fraction$

Perhatikan perhitungan berikut.

$table attributes columnalign right center left columnspacing 2px end attributes row cell limit as x rightwards arrow 0 of space fraction numerator tan space x over denominator x squared minus 3 x end fraction end cell equals cell limit as x rightwards arrow 0 of space fraction numerator open parentheses begin display style fraction numerator straight d over denominator straight d x end fraction end style open parentheses tan space x close parentheses close parentheses over denominator open parentheses fraction numerator straight d over denominator straight d x end fraction open parentheses x squared minus 3 x close parentheses close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of space fraction numerator sec squared space x over denominator 2 x minus 3 end fraction end cell row blank equals cell fraction numerator sec squared space open parentheses 0 close parentheses over denominator 2 open parentheses 0 close parentheses minus 3 end fraction end cell row blank equals cell fraction numerator 1 over denominator 0 minus 3 end fraction end cell row cell limit as x rightwards arrow 0 of space fraction numerator tan space x over denominator x squared minus 3 x end fraction end cell equals cell negative 1 third end cell end table$

Jadi, jawaban yang tepat adalah D.