Pertanyaan

x → 2 lim 3 x − 2 − x + 2 x − 2 = ...

$x \to 2 lim \frac{x - 2}{3 x - 2 - x + 2} =$ ...

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Kalikan limit dengan akar sekawan seperti berikut: Kemudian substitusi ke persamaan limit seperti berikut: Jadi, jawaban yang tepat adalah B.

Kalikan limit dengan akar sekawan seperti berikut:

$begin mathsize 14px style table attributes columnalign left center center end attributes row cell limit as x rightwards arrow 2 of space fraction numerator x minus 2 over denominator square root of 3 x minus 2 end root minus square root of x plus 2 end root end fraction cross times fraction numerator square root of 3 x minus 2 end root plus square root of x plus 2 end root over denominator square root of 3 x minus 2 end root plus square root of x plus 2 end root end fraction end cell space space row cell limit as x rightwards arrow 2 of space fraction numerator x minus 2 open parentheses square root of 3 x minus 2 end root plus square root of x plus 2 end root close parentheses over denominator open parentheses square root of 3 x minus 2 end root minus square root of x plus 2 end root close parentheses cross times open parentheses square root of 3 x minus 2 end root plus square root of x plus 2 end root close parentheses end fraction end cell space space row cell limit as x rightwards arrow 2 of space fraction numerator x minus 2 open parentheses square root of 3 x minus 2 end root plus square root of x plus 2 end root close parentheses over denominator 3 x minus 2 minus open parentheses x plus 2 close parentheses end fraction end cell space space row cell limit as x rightwards arrow 2 of space fraction numerator x minus 2 open parentheses square root of 3 x minus 2 end root plus square root of x plus 2 end root close parentheses over denominator 3 x minus x minus 2 minus 2 end fraction end cell space space row cell limit as x rightwards arrow 2 of space fraction numerator x minus 2 open parentheses square root of 3 x minus 2 end root plus square root of x plus 2 end root close parentheses over denominator 2 x minus 4 end fraction end cell space space row cell limit as x rightwards arrow 2 of space fraction numerator down diagonal strike x minus 2 end strike open parentheses square root of 3 x minus 2 end root plus square root of x plus 2 end root close parentheses over denominator 2 down diagonal strike open parentheses x minus 2 close parentheses end strike end fraction end cell space space row cell limit as x rightwards arrow 2 of space fraction numerator open parentheses square root of 3 x minus 2 end root plus square root of x plus 2 end root close parentheses over denominator 2 end fraction end cell space space end table end style$

Kemudian substitusi ke persamaan limit seperti berikut:

$begin mathsize 14px style table attributes columnalign center center left end attributes row cell limit as x rightwards arrow 2 of space fraction numerator square root of 3 x minus 2 end root plus square root of x plus 2 end root over denominator 2 end fraction end cell equals cell fraction numerator square root of 3 open parentheses 2 close parentheses minus 2 end root plus square root of 2 plus 2 end root over denominator 2 end fraction end cell row space equals cell fraction numerator square root of 6 minus 2 end root plus square root of 4 over denominator 2 end fraction end cell row space equals cell fraction numerator square root of 4 plus 2 over denominator 2 end fraction end cell row space equals cell fraction numerator 2 plus 2 over denominator 2 end fraction end cell row space equals cell 4 over 2 end cell row space equals 2 end table end style$

Jadi, jawaban yang tepat adalah B.