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Nilai dari .

Nilai dari limit as x rightwards arrow 0 of space fraction numerator tan space x over denominator x squared minus 3 x end fraction equals....

  1. 1 third 

  2. 1 half 

  3. negative 1 half 

  4. negative 1 third 

  5. negative 1 

Jawaban:

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.

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