Pertanyaan

x → 3 lim x + 4 − 2 x + 1 x − 3

$x \to 3 lim \frac{x - 3}{x + 4 - 2 x + 1}$

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Habis dalam

Klaim

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

nilai dari adalah

nilai dari $begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x minus 3 over denominator square root of x plus 4 end root minus square root of 2 x plus 1 end root end fraction end style$ adalah

Pembahasan

Bentuk limit pada soal bisa kita selesaikan dengan dikalikan akar sekawan sebagai berikut: Jadi, nilai dari adalah

Bentuk limit pada soal bisa kita selesaikan dengan dikalikan akar sekawan sebagai berikut:

$begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x minus 3 over denominator square root of x plus 4 end root minus square root of 2 x plus 1 end root end fraction equals limit as x rightwards arrow 3 of fraction numerator x minus 3 over denominator square root of x plus 4 end root minus square root of 2 x plus 1 end root end fraction cross times fraction numerator square root of x plus 4 end root plus square root of 2 x plus 1 end root over denominator square root of x plus 4 end root plus square root of 2 x plus 1 end root end fraction equals limit as x rightwards arrow 3 of fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis square root of x plus 4 end root plus square root of 2 x plus 1 end root right parenthesis over denominator left parenthesis x plus 4 right parenthesis minus open parentheses 2 x plus 1 close parentheses end fraction equals limit as x rightwards arrow 3 of fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis square root of x plus 4 end root plus square root of 2 x plus 1 end root right parenthesis over denominator x plus 4 minus 2 x minus 1 end fraction equals limit as x rightwards arrow 3 of fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis square root of x plus 4 end root plus square root of 2 x plus 1 end root right parenthesis over denominator negative x plus 3 end fraction equals limit as x rightwards arrow 3 of fraction numerator up diagonal strike left parenthesis x minus 3 right parenthesis end strike left parenthesis square root of x plus 4 end root plus square root of 2 x plus 1 end root right parenthesis over denominator negative up diagonal strike left parenthesis x minus 3 right parenthesis end strike end fraction equals limit as x rightwards arrow 3 of minus left parenthesis square root of x plus 4 end root plus square root of 2 x plus 1 end root right parenthesis equals negative left parenthesis square root of 3 plus 4 end root plus square root of 2 left parenthesis 3 right parenthesis plus 1 end root right parenthesis equals negative left parenthesis square root of 7 plus square root of 7 right parenthesis equals negative 2 square root of 7 end style$

Jadi, nilai dari $begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x minus 3 over denominator square root of x plus 4 end root minus square root of 2 x plus 1 end root end fraction end style$ adalah