Pertanyaan

x → 2 lim 4 x + 1 − 7 x − 5 5 x − 1 − 2 x + 5

$x \to 2 lim \frac{5 x - 1 - 2 x + 5}{4 x + 1 - 7 x - 5}$

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Habis dalam

Klaim

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

hasil dari adalah .

hasil dari $limit as x rightwards arrow 2 of fraction numerator square root of 5 x minus 1 end root minus square root of 2 x plus 5 end root over denominator square root of 4 x plus 1 end root minus square root of 7 x minus 5 end root end fraction$ adalah negative 1

Pembahasan

Perhitungan dapat dilakukan dengan aturan L hospital, sehingga : Jadi, hasil dari adalah .

Perhitungan dapat dilakukan dengan aturan L hospital, sehingga :

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator square root of 5 x minus 1 end root minus square root of 2 x plus 5 end root over denominator square root of 4 x plus 1 end root minus square root of 7 x minus 5 end root end fraction end cell equals cell limit as x rightwards arrow 2 of open parentheses fraction numerator begin display style fraction numerator 5 over denominator 2 square root of 5 x minus 1 end root end fraction end style minus begin display style fraction numerator 1 over denominator square root of 2 x plus 5 end root end fraction end style over denominator begin display style fraction numerator 2 over denominator square root of 4 x plus 1 end root end fraction end style minus begin display style fraction numerator 7 over denominator 2 square root of 7 x minus 5 end root end fraction end style end fraction close parentheses end cell row blank equals cell fraction numerator begin display style fraction numerator 5 over denominator 2 square root of 5 left parenthesis 2 right parenthesis minus 1 end root end fraction minus fraction numerator 1 over denominator square root of 2 left parenthesis 2 right parenthesis plus 5 end root end fraction end style over denominator begin display style fraction numerator 2 over denominator square root of 4 left parenthesis 2 right parenthesis plus 1 end root end fraction minus fraction numerator 7 over denominator 2 square root of 7 left parenthesis 2 right parenthesis minus 5 end root end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 5 over denominator 2 square root of 10 minus 1 end root end fraction minus fraction numerator 1 over denominator square root of 4 plus 5 end root end fraction end style over denominator begin display style fraction numerator 2 over denominator square root of 8 plus 1 end root end fraction minus fraction numerator 7 over denominator 2 square root of 14 minus 5 end root end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 5 over denominator 2 square root of 9 end fraction minus fraction numerator 1 over denominator square root of 9 end fraction end style over denominator begin display style fraction numerator 2 over denominator square root of 9 end fraction minus fraction numerator 7 over denominator 2 square root of 9 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 5 over denominator 2 times 3 end fraction minus 1 third end style over denominator begin display style 2 over 3 minus fraction numerator 7 over denominator 2 times 3 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style 5 over 6 end style minus begin display style 1 third end style over denominator begin display style 2 over 3 end style minus begin display style 7 over 6 end style end fraction end cell row blank equals cell fraction numerator begin display style 5 over 6 minus 2 over 6 end style over denominator begin display style 4 over 6 minus 7 over 6 end style end fraction end cell row blank equals cell fraction numerator begin display style 3 over 6 end style over denominator begin display style fraction numerator negative 3 over denominator 6 end fraction end style end fraction end cell row blank equals cell 3 over 6 cross times fraction numerator negative 6 over denominator 3 end fraction end cell row blank equals cell fraction numerator negative 18 over denominator 18 end fraction end cell row blank equals cell negative 1 end cell end table$

Jadi, hasil dari $limit as x rightwards arrow 2 of fraction numerator square root of 5 x minus 1 end root minus square root of 2 x plus 5 end root over denominator square root of 4 x plus 1 end root minus square root of 7 x minus 5 end root end fraction$ adalah negative 1 .