Pertanyaan

x → 0 lim x + 3 − x − 3 x 2 + 2 x + 3 − x 2 − 2 x + 3

$x \to 0 lim \frac{x ^{2} + 2 x + 3 - x ^{2} - 2 x + 3}{x + 3 - x - 3}$

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Habis dalam

Klaim

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai adalah .

nilai $begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator square root of x squared plus 2 x plus 3 end root minus square root of x squared plus 2 x plus 3 end root over denominator square root of x plus 3 end root minus square root of x minus 3 end root end fraction end style$ adalah

Pembahasan

Menyelesaikan limit dengan mengalikan akar sekawan, diperoleh Jadi, nilai adalah .

Menyelesaikan limit dengan mengalikan akar sekawan, diperoleh

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator square root of x squared plus 2 x plus 3 end root minus square root of x squared minus 2 x plus 3 end root over denominator square root of x plus 3 end root minus square root of x minus 3 end root end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator square root of x squared plus 2 x plus 3 end root minus square root of x squared minus 2 x plus 3 end root over denominator square root of x plus 3 end root minus square root of x minus 3 end root end fraction times fraction numerator square root of x plus 3 end root plus square root of x minus 3 end root over denominator square root of x plus 3 end root plus square root of x minus 3 end root end fraction times fraction numerator square root of x squared plus 2 x plus 3 end root plus square root of x squared minus 2 x plus 3 end root over denominator square root of x squared plus 2 x plus 3 end root plus square root of x squared minus 2 x plus 3 end root end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x squared plus 2 x plus 3 minus x squared plus 2 x minus 3 over denominator x plus 3 minus x plus 3 end fraction times fraction numerator square root of x plus 3 end root plus square root of x minus 3 end root over denominator square root of x squared plus 2 x plus 3 end root plus square root of x squared plus 2 x plus 3 end root end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 4 x over denominator 6 end fraction times fraction numerator square root of x plus 3 end root plus square root of x minus 3 end root over denominator square root of x squared plus 2 x plus 3 end root plus square root of x squared plus 2 x plus 3 end root end fraction end cell row blank equals cell fraction numerator 4 open parentheses 0 close parentheses over denominator 6 end fraction times fraction numerator square root of 0 plus 3 end root plus square root of 0 minus 3 end root over denominator square root of 0 squared plus 2 open parentheses 0 close parentheses plus 3 end root plus square root of x squared plus 2 open parentheses 0 close parentheses plus 3 end root end fraction end cell row blank equals 0 end table end style$

Jadi, nilai $begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator square root of x squared plus 2 x plus 3 end root minus square root of x squared plus 2 x plus 3 end root over denominator square root of x plus 3 end root minus square root of x minus 3 end root end fraction end style$ adalah .