Tentukan nilai limit berikut! x→1lim3x+1−2x−1

Pertanyaan

Tentukan nilai limit berikut!

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

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L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator x minus 1 over denominator square root of 3 x plus 1 end root minus 2 end fraction end cell equals cell limit as x rightwards arrow 1 of open parentheses fraction numerator x minus 1 over denominator square root of 3 x plus 1 end root minus 2 end fraction close parentheses times open parentheses fraction numerator square root of 3 x plus 1 end root plus 2 over denominator square root of 3 x plus 1 end root plus 2 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator open parentheses x minus 1 close parentheses open parentheses square root of 3 x plus 1 end root plus 2 close parentheses over denominator open parentheses 3 x plus 1 close parentheses minus open parentheses 4 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator left parenthesis x minus 1 right parenthesis left parenthesis square root of 3 x plus 1 end root plus 2 right parenthesis over denominator 3 x minus 3 end fraction space end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator left parenthesis x minus 1 right parenthesis left parenthesis square root of 3 x plus 1 end root plus 2 right parenthesis over denominator 3 open parentheses x minus 1 close parentheses end fraction space end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator square root of 3 x plus 1 end root plus 2 over denominator 3 end fraction space end cell row blank equals cell fraction numerator square root of 3 open parentheses 1 close parentheses plus 1 end root plus 2 over denominator 3 end fraction end cell row blank equals cell 4 over 3 end cell end table end style$