Pertanyaan

x → 3 lim x 2 + 7 − 4 x 2 − 9

$x \to 3 lim \frac{x ^{2} - 9}{x ^{2} + 7 - 4}$

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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.

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.