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x→∞lim​7x2+2x−6​3x−5​=

Pertanyaan

limit as x rightwards arrow infinity of fraction numerator 3 x minus 5 over denominator square root of 7 x squared plus 2 x minus 6 end root end fraction equals 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

 limit as x rightwards arrow infinity thin space of open parentheses fraction numerator 3 x minus 5 over denominator square root of 7 x squared plus 2 x minus 6 end root end fraction close parentheses equals fraction numerator 3 square root of 7 over denominator 7 end fraction.

Pembahasan

Ingat bahwa:

  • limit as x rightwards arrow a of open square brackets fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction close square brackets equals fraction numerator lim subscript x rightwards arrow a end subscript f open parentheses x close parentheses over denominator lim subscript x rightwards arrow a end subscript g open parentheses x close parentheses end fraction comma thin space    limit as x rightwards arrow a of g open parentheses x close parentheses not equal to 0 

Sehingga,

limit as x rightwards arrow infinity thin space of open parentheses fraction numerator 3 x minus 5 over denominator square root of 7 x squared plus 2 x minus 6 end root end fraction close parentheses equals limit as x rightwards arrow infinity thin space of open parentheses fraction numerator begin display style fraction numerator 3 x over denominator x end fraction end style minus begin display style 5 over x end style over denominator square root of begin display style fraction numerator 7 x squared over denominator x squared end fraction end style plus fraction numerator 2 x over denominator x squared end fraction minus 6 over x squared end root end fraction close parentheses equals limit as x rightwards arrow infinity thin space of open parentheses fraction numerator 3 minus 5 over x over denominator square root of 7 plus 2 over x minus 6 over x squared end root end fraction close parentheses equals fraction numerator lim subscript x rightwards arrow infinity thin space end subscript open parentheses 3 minus 5 over x close parentheses over denominator lim subscript x rightwards arrow infinity thin space end subscript open parentheses square root of 7 plus 2 over x minus 6 over x squared end root close parentheses end fraction equals fraction numerator open parentheses 3 minus 5 over infinity close parentheses over denominator square root of 7 plus 2 over infinity minus 6 over infinity squared end root end fraction equals fraction numerator 3 square root of 7 over denominator 7 end fraction 

Jadi, limit as x rightwards arrow infinity thin space of open parentheses fraction numerator 3 x minus 5 over denominator square root of 7 x squared plus 2 x minus 6 end root end fraction close parentheses equals fraction numerator 3 square root of 7 over denominator 7 end fraction.

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