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Nilai dari

Pertanyaan

Nilai dari begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator 5 x over denominator 3 minus square root of 9 plus x end root end fraction equals... end style

Pembahasan Soal:

Langkah awal menentukan nilai limit adalah dengan mensubstitusi nilai x, maka

begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator 5 x over denominator 3 minus square root of 9 plus x end root end fraction equals 0 over 0 end style

Setelah disubstitusi ternyata diperoleh bentuk tak tentu, sehingga untuk menyelesaikannya digunakan metode pemfaktoran

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator 5 x over denominator 3 minus square root of 9 plus x end root end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator 5 x over denominator 3 minus square root of 9 plus x end root end fraction times fraction numerator 3 plus square root of 9 plus x end root over denominator 3 plus square root of 9 plus x end root end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 5 x times open parentheses 3 plus square root of 9 plus x end root close parentheses over denominator 9 minus left parenthesis 9 plus x right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 5 x times open parentheses 3 plus square root of 9 plus x end root close parentheses over denominator negative x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of minus 5 open parentheses 3 plus square root of 9 plus x end root close parentheses end cell row blank equals cell negative 5 open parentheses 3 plus square root of 9 plus 0 end root close parentheses end cell row blank equals cell negative 30 end cell end table end style

Jadi, diperoleh begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 5 x over denominator 3 minus square root of 9 plus x end root end fraction end cell end table equals negative 30 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 Maret 2021

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