Pertanyaan

Nilai x → 1 lim 1 − x ( 5 − x − 2 ) ( 2 − x + 1 ) adalah...

Nilai $x \to 1 lim \frac{( 5 - x - 2 ) ( 2 - x + 1 )}{1 - x}$ adalah...

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

maka limit tersebutharus dirasionalkan terlebih dahulu, yaitu:

$limit as x rightwards arrow 1 of fraction numerator open parentheses square root of 5 minus x end root minus 2 close parentheses open parentheses square root of 2 minus x end root plus 1 close parentheses over denominator 1 minus x end fraction equals fraction numerator open parentheses square root of 5 minus 1 end root minus 2 close parentheses open parentheses square root of 2 minus 1 end root plus 1 close parentheses over denominator 1 minus 1 end fraction equals 0 over 0$

maka limit tersebut harus dirasionalkan terlebih dahulu, yaitu:

$begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator open parentheses square root of 5 minus x end root minus 2 close parentheses open parentheses square root of 2 minus x end root plus 1 close parentheses over denominator 1 minus x end fraction cross times fraction numerator open parentheses square root of 5 minus x end root plus 2 close parentheses over denominator open parentheses square root of 5 minus x end root plus 2 close parentheses end fraction equals limit as x rightwards arrow 1 of fraction numerator open parentheses open parentheses 5 minus x close parentheses minus 4 close parentheses open parentheses square root of 2 minus x end root plus 1 close parentheses over denominator open parentheses 1 minus x close parentheses open parentheses square root of 5 minus x end root plus 2 close parentheses end fraction equals limit as x rightwards arrow 1 of fraction numerator up diagonal strike open parentheses 1 minus x close parentheses end strike open parentheses square root of 2 minus x end root plus 1 close parentheses over denominator up diagonal strike open parentheses 1 minus x close parentheses end strike open parentheses square root of 5 minus x end root plus 2 close parentheses end fraction equals limit as x rightwards arrow 1 of fraction numerator open parentheses square root of 2 minus x end root plus 1 close parentheses over denominator open parentheses square root of 5 minus x end root plus 2 close parentheses end fraction equals fraction numerator open parentheses square root of 2 minus 1 end root plus 1 close parentheses over denominator open parentheses square root of 5 minus 1 end root plus 2 close parentheses end fraction equals fraction numerator 1 plus 1 over denominator 2 plus 2 end fraction equals 2 over 4 equals 1 half end style$

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