Pertanyaan

x → 2 lim x − 2 4 x + 1 − 3 x + 3 = ...

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

R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

$limit as x rightwards arrow 2 of space fraction numerator square root of 4 x plus 1 end root minus square root of 3 x plus 3 end root over denominator x minus 2 end fraction equals 1 over 6.$

Pembahasan

Perhatikan penghitungan berikut! Jadi,

Perhatikan penghitungan berikut!

$limit as x rightwards arrow 2 of space fraction numerator square root of 4 x plus 1 end root minus square root of 3 x plus 3 end root over denominator x minus 2 end fraction equals limit as x rightwards arrow 2 of space fraction numerator square root of 4 x plus 1 end root minus square root of 3 x plus 3 end root over denominator x minus 2 end fraction cross times fraction numerator square root of 4 x plus 1 end root plus square root of 3 x plus 3 end root over denominator square root of 4 x plus 1 end root plus square root of 3 x plus 3 end root end fraction equals limit as x rightwards arrow 2 of space fraction numerator open parentheses square root of 4 x plus 1 end root close parentheses squared minus open parentheses square root of 3 x plus 3 end root close parentheses squared over denominator open parentheses x minus 2 close parentheses open parentheses square root of 4 x plus 1 end root plus square root of 3 x plus 3 end root close parentheses end fraction equals limit as x rightwards arrow 2 of space fraction numerator open parentheses 4 x plus 1 close parentheses minus open parentheses 3 x plus 3 close parentheses over denominator open parentheses x minus 2 close parentheses open parentheses square root of 4 x plus 1 end root plus square root of 3 x plus 3 end root close parentheses end fraction equals limit as x rightwards arrow 2 of space fraction numerator up diagonal strike open parentheses x minus 2 close parentheses end strike over denominator up diagonal strike open parentheses x minus 2 close parentheses end strike open parentheses square root of 4 x plus 1 end root plus square root of 3 x plus 3 end root close parentheses end fraction equals limit as x rightwards arrow 2 of space fraction numerator 1 over denominator open parentheses square root of 4 x plus 1 end root plus square root of 3 x plus 3 end root close parentheses end fraction equals fraction numerator 1 over denominator open parentheses square root of 4 open parentheses 2 close parentheses plus 1 end root plus square root of 3 open parentheses 2 close parentheses plus 3 end root close parentheses end fraction equals fraction numerator 1 over denominator open parentheses square root of 9 plus square root of 9 close parentheses end fraction equals fraction numerator 1 over denominator 3 plus 3 end fraction equals 1 over 6 Note colon open parentheses a minus b close parentheses open parentheses a plus b close parentheses equals a squared minus b squared open parentheses square root of 4 x plus 1 end root minus square root of 3 x plus 3 end root close parentheses open parentheses square root of 4 x plus 1 end root plus square root of 3 x plus 3 end root close parentheses equals open parentheses square root of 4 x plus 1 end root close parentheses squared minus open parentheses square root of 3 x plus 3 end root close parentheses squared equals open parentheses 4 x plus 1 close parentheses minus open parentheses 3 x plus 3 close parentheses equals x minus 2$

Jadi, $limit as x rightwards arrow 2 of space fraction numerator square root of 4 x plus 1 end root minus square root of 3 x plus 3 end root over denominator x minus 2 end fraction equals 1 over 6.$