Pertanyaan

Nilai dari x → 7 lim x + 2 − 3 x − 2 x − 2 adalah ....

Nilai dari $x \to 7 lim \frac{x - 2}{x + 2 - 3 x - 2}$ adalah ....

$begin mathsize 14px style fraction numerator 3 plus square root of 19 over denominator 2 end fraction end style$
$begin mathsize 14px style fraction numerator negative 3 minus square root of 19 over denominator 2 end fraction end style$
$begin mathsize 14px style fraction numerator negative 3 plus square root of 19 over denominator 2 end fraction end style$

R. Risda

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Ingat sifat aljabar a 2 − b 2 = ( a + b ) ( a − b ) ! Kemudian, perhatikan perhitungan berikut ini! Dengan demikian, nilai dari adalah . Jadi, jawaban yang tepat adalah D.

Ingat sifat aljabar $a^{2} - b^{2} = (a + b) (a - b)$ !

Kemudian, perhatikan perhitungan berikut ini!

$begin mathsize 14px style limit as x rightwards arrow 7 of invisible function application blank blank fraction numerator x minus 2 over denominator square root of x plus 2 end root minus square root of 3 x minus 2 end root end fraction equals blank limit as x rightwards arrow 7 of fraction numerator x minus 2 over denominator square root of x plus 2 end root minus square root of 3 x minus 2 end root end fraction. fraction numerator square root of x plus 2 end root plus square root of 3 x minus 2 end root over denominator square root of x plus 2 end root plus square root of 3 x minus 2 end root end fraction equals limit as x rightwards arrow 7 of fraction numerator left parenthesis x minus 2 right parenthesis open parentheses square root of x plus 2 end root plus square root of 3 x minus 2 end root close parentheses over denominator left parenthesis x plus 2 right parenthesis minus left parenthesis 3 x minus 2 right parenthesis end fraction equals limit as x rightwards arrow 7 of fraction numerator left parenthesis x minus 2 right parenthesis open parentheses square root of x plus 2 end root plus square root of 3 x minus 2 end root close parentheses over denominator negative 2 x plus 4 end fraction equals limit as x rightwards arrow 7 of fraction numerator up diagonal strike left parenthesis x minus 2 right parenthesis end strike open parentheses square root of x plus 2 end root plus square root of 3 x minus 2 end root close parentheses over denominator left parenthesis negative 2 right parenthesis up diagonal strike left parenthesis x minus 2 right parenthesis end strike end fraction equals fraction numerator square root of 7 plus 2 end root plus square root of 3 left parenthesis 7 right parenthesis minus 2 end root over denominator negative 2 end fraction equals fraction numerator square root of 9 plus square root of 19 over denominator negative 2 end fraction equals fraction numerator 3 plus square root of 19 over denominator negative 2 end fraction equals minus fraction numerator open parentheses 3 plus square root of 19 close parentheses over denominator 2 end fraction equals fraction numerator negative 3 minus square root of 19 over denominator 2 end fraction end style$

Dengan demikian, nilai dari $begin mathsize 14px style limit as x rightwards arrow 7 of invisible function application blank fraction numerator x minus 2 over denominator square root of x plus 2 end root minus square root of 3 x minus 2 end root end fraction end style$ adalah $begin mathsize 14px style fraction numerator negative 3 minus square root of 19 over denominator 2 end fraction end style$ .

Jadi, jawaban yang tepat adalah D.