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Pertanyaan

x → 3 lim ​ x 2 + 7 ​ − 4 x 2 − 9 ​

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S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

adalah 8.

 begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator square root of x squared plus 7 end root minus 4 end fraction end style adalah 8.

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Pembahasan

Perhitungan limit fungsi dapat dilakukan dengan metodemengalikan akar sekawan. Dengan mengalikan akar sekawan Jadi, adalah 8.

Perhitungan limit fungsi begin mathsize 14px style f open parentheses x close parentheses space text untuk  end text x text →a, a≠0 end text end style dapat dilakukan dengan metode mengalikan akar sekawan.

Dengan mengalikan akar sekawan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator square root of x squared plus 7 end root minus 4 end fraction end cell equals cell 0 over 0 end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator square root of x squared plus 7 end root minus 4 end fraction cross times fraction numerator square root of x squared plus 7 end root plus 4 over denominator square root of x squared plus 7 end root plus 4 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses x squared minus 9 close parentheses cross times open parentheses square root of x squared plus 7 end root plus 4 close parentheses over denominator open parentheses x squared plus 7 close parentheses minus 16 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator up diagonal strike left parenthesis x squared minus 9 right parenthesis end strike cross times left parenthesis square root of x squared plus 7 end root plus 4 right parenthesis over denominator blank end fraction end cell row blank equals cell limit as x rightwards arrow 3 of square root of x squared plus 7 end root plus 4 end cell row blank equals cell square root of 3 squared plus 7 end root plus 4 end cell row blank equals cell square root of 16 plus 4 end cell row blank equals cell 4 plus 4 end cell row blank equals 8 end table end style

Jadi, begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator square root of x squared plus 7 end root minus 4 end fraction end style adalah 8.

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