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Pertanyaan

x → 9 lim ​ x ​ − 3 x 2 − 7 x − 18 ​

 

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D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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diperoleh .

diperoleh limit as x rightwards arrow 9 of space fraction numerator x squared minus 7 x minus 18 over denominator square root of x minus 3 end fraction equals 66.

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Pembahasan

Gunakan konsep menentukan nilai limit dengan mengalikan dengan akar sekawan. Perhatikan perhitungan berikut. Jadi, diperoleh .

Gunakan konsep menentukan nilai limit dengan mengalikan dengan akar sekawan.

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell limit as x rightwards arrow 9 of space fraction numerator x squared minus 7 x minus 18 over denominator square root of x minus 3 end fraction end cell equals cell limit as x rightwards arrow 9 of space fraction numerator x squared minus 7 x minus 18 over denominator square root of x minus 3 end fraction cross times fraction numerator square root of x plus 3 over denominator square root of x plus 3 end fraction end cell row blank equals cell limit as x rightwards arrow 9 of space fraction numerator open parentheses x squared minus 7 x minus 18 close parentheses open parentheses square root of x plus 3 close parentheses over denominator open parentheses square root of x minus 3 close parentheses open parentheses square root of x plus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 9 of space fraction numerator up diagonal strike open parentheses x minus 9 close parentheses end strike open parentheses x plus 2 close parentheses open parentheses square root of x plus 3 close parentheses over denominator up diagonal strike open parentheses x minus 9 close parentheses end strike end fraction end cell row blank equals cell limit as x rightwards arrow 9 of space open parentheses x plus 2 close parentheses open parentheses square root of x plus 3 close parentheses end cell row blank equals cell open parentheses 9 plus 2 close parentheses open parentheses square root of 9 plus 3 close parentheses end cell row blank equals cell open parentheses 11 close parentheses open parentheses 3 plus 3 close parentheses end cell row blank equals cell 11 cross times 6 end cell row blank equals 66 end table

Jadi, diperoleh limit as x rightwards arrow 9 of space fraction numerator x squared minus 7 x minus 18 over denominator square root of x minus 3 end fraction equals 66.

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