Pertanyaan

Nilai x → 2 lim ( 2 − x + 2 x − 2 ) = ...

Nilai $x \to 2 lim (\frac{x - 2}{2 - x + 2}) = ...$

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Mencari hasil limit: Jadi, . Dengan demikian, jawaban yang tepat adalah B.

Mencari hasil limit:

$limit as x rightwards arrow thin space 2 of open parentheses fraction numerator x minus 2 over denominator 2 minus square root of x plus 2 end root end fraction close parentheses equals limit as x rightwards arrow thin space 2 of open parentheses fraction numerator x minus 2 over denominator 2 minus square root of x plus 2 end root end fraction cross times fraction numerator 2 plus square root of x plus 2 end root over denominator 2 plus square root of x plus 2 end root end fraction close parentheses equals limit as x rightwards arrow thin space 2 of open parentheses fraction numerator x minus 2 over denominator 2 minus square root of x plus 2 end root end fraction cross times fraction numerator 2 plus square root of x plus 2 end root over denominator 2 plus square root of x plus 2 end root end fraction close parentheses equals limit as x rightwards arrow thin space 2 of open parentheses fraction numerator x minus 2 open parentheses 2 plus square root of x plus 2 end root close parentheses over denominator 2 minus square root of x plus 2 end root open parentheses 2 plus square root of x plus 2 end root close parentheses end fraction close parentheses equals limit as x rightwards arrow thin space 2 of open parentheses fraction numerator x minus 2 open parentheses 2 plus square root of x plus 2 end root close parentheses over denominator negative left parenthesis x minus 2 right parenthesis end fraction close parentheses equals limit as x rightwards arrow thin space 2 of open parentheses negative open parentheses 2 plus square root of x plus 2 end root close parentheses close parentheses equals negative open parentheses 2 plus square root of 2 plus 2 end root close parentheses equals negative open parentheses 2 plus square root of 4 close parentheses equals negative open parentheses 2 plus 2 close parentheses equals negative 4$

Jadi, $limit as x rightwards arrow thin space 2 of open parentheses fraction numerator x minus 2 over denominator 2 minus square root of x plus 2 end root end fraction close parentheses equals negative 4$ .

Dengan demikian, jawaban yang tepat adalah B.