Pertanyaan

Soal UN 2017 Nilai dari lim x → 2 x 2 − 6 x + 8 2 − x + 2 adalah...

Soal UN 2017

Nilai dari $lim_{x \to 2} \frac{2 - x + 2}{x ^{2} - 6 x + 8}$ adalah...

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

$limit as straight x rightwards arrow 2 of space space fraction numerator 2 minus square root of x plus 2 end root over denominator x squared minus 6 x plus 8 end fraction equals limit as x rightwards arrow 2 of space fraction numerator 2 minus square root of x plus 2 end root over denominator x squared minus 6 x plus 8 end fraction space. space space fraction numerator 2 plus square root of x plus 2 end root over denominator 2 plus square root of x plus 2 end root end fraction equals limit as x rightwards arrow 2 of fraction numerator 4 minus open parentheses x plus 2 close parentheses over denominator left parenthesis x minus 4 right parenthesis left parenthesis x minus 2 right parenthesis open parentheses 2 plus square root of x plus 2 end root close parentheses end fraction equals limit as x rightwards arrow 2 of fraction numerator 2 minus x over denominator left parenthesis x minus 4 right parenthesis left parenthesis x minus 2 right parenthesis open parentheses 2 plus square root of x plus 2 end root close parentheses end fraction equals limit as x rightwards arrow 2 of fraction numerator horizontal strike 2 minus x end strike space space to the power of negative 1 end exponent over denominator open parentheses x minus 4 close parentheses horizontal strike open parentheses x minus 2 close parentheses end strike open parentheses 2 plus square root of x plus 2 end root close parentheses end fraction equals fraction numerator negative 1 over denominator left parenthesis 2 minus 4 right parenthesis left parenthesis 2 plus square root of 2 plus 2 end root space right parenthesis end fraction equals space fraction numerator negative 1 over denominator open parentheses negative 2 close parentheses open parentheses 2 plus 2 close parentheses end fraction equals 1 over 8 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space$