Pertanyaan

Tentukan nilai dari x → 1 lim 1 − x x + 2 − 4 x − 1 !

Tentukan nilai dari $x \to 1 lim \frac{x + 2 - 4 x - 1}{1 - x}$ !

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Habis dalam

Klaim

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari $begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator square root of x plus 2 end root minus square root of 4 x minus 1 end root over denominator 1 minus x end fraction end style$ adalah $begin mathsize 14px style fraction numerator square root of 3 over denominator 2 end fraction end style$ .

Pembahasan

Diketahui: Limit fungsi . Limit fungsi adalah perilaku suatu fungsi mendekati suatu nilai tertentu. Untuk mengerjakan soal limit fungsi akar bentuk rasional dapat menggunakan metode perkalian akar sekawan dan pemfaktoran seperti penyelesaian di bawah ini: Kemudian substitusi ke limit fungsi. Dengan demikian, nilai dari adalah .

Diketahui:

Limit fungsi $begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator square root of x plus 2 end root minus square root of 4 x minus 1 end root over denominator 1 minus x end fraction end style$ .

Limit fungsi adalah perilaku suatu fungsi mendekati suatu nilai tertentu.

Untuk mengerjakan soal limit fungsi akar bentuk rasional dapat menggunakan metode perkalian akar sekawan dan pemfaktoran seperti penyelesaian di bawah ini:

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

Kemudian substitusi ke limit fungsi.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator 3 over denominator square root of x plus 2 end root plus square root of 4 x minus 1 end root end fraction end cell equals cell fraction numerator 3 over denominator square root of 1 plus 2 end root plus square root of 4 open parentheses 1 close parentheses minus 1 end root end fraction end cell row blank equals cell fraction numerator 3 over denominator square root of 3 plus square root of 4 minus 1 end root end fraction end cell row blank equals cell fraction numerator 3 over denominator square root of 3 plus square root of 3 end fraction end cell row blank equals cell fraction numerator 3 over denominator 2 square root of 3 end fraction end cell row blank equals cell fraction numerator 3 over denominator 2 square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator 3 square root of 3 over denominator 2 cross times 3 end fraction end cell row blank equals cell fraction numerator 3 square root of 3 over denominator 6 end fraction end cell row blank equals cell fraction numerator square root of 3 over denominator 2 end fraction end cell end table end style$

Dengan demikian, nilai dari $begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator square root of x plus 2 end root minus square root of 4 x minus 1 end root over denominator 1 minus x end fraction end style$ adalah $begin mathsize 14px style fraction numerator square root of 3 over denominator 2 end fraction end style$ .