Pertanyaan

x → 0 lim ( 1 − 2 x − 1 + 2 x 2 1 + 2 x − 1 − 2 x 2 ) = ...

$x \to 0 lim (\frac{1 + 2 x - 1 - 2 x ^{2}}{1 - 2 x - 1 + 2 x ^{2}}) = ...$

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Klaim

O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

Pembahasan

Menentukan limit dengan mengalikan akar sekawan: Hasil dari limit tersebut adalah tidak terdefinisi.

Menentukan limit dengan mengalikan akar sekawan:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of open parentheses fraction numerator square root of 1 plus 2 x end root minus square root of 1 minus 2 x squared end root over denominator square root of 1 minus 2 x end root minus square root of 1 plus 2 x squared end root end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 0 of open parentheses fraction numerator square root of 1 plus 2 x end root minus square root of 1 minus 2 x squared end root over denominator square root of 1 minus 2 x end root minus square root of 1 plus 2 x squared end root end fraction close parentheses cross times open parentheses fraction numerator square root of 1 minus 2 x end root plus square root of 1 plus 2 x squared end root over denominator square root of 1 minus 2 x end root plus square root of 1 plus 2 x squared end root end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 0 of open parentheses fraction numerator 1 minus 2 x minus square root of open parentheses 1 minus 2 x squared close parentheses open parentheses 1 minus 2 x close parentheses end root minus square root of open parentheses 1 minus 2 x squared close parentheses open parentheses 1 plus 2 x squared close parentheses end root over denominator 1 minus 2 x minus open parentheses 1 plus 2 x squared close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 0 of open parentheses fraction numerator 1 minus 2 x minus square root of 1 minus 2 x squared minus 2 x plus 4 x cubed end root minus square root of 1 minus 4 x to the power of 4 end root over denominator negative 2 x minus 2 x squared end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 1 minus 2 left parenthesis 0 right parenthesis minus square root of 1 minus 2 left parenthesis 0 right parenthesis squared minus 2 left parenthesis 0 right parenthesis plus 4 left parenthesis 0 right parenthesis cubed end root minus square root of 1 minus 4 left parenthesis 0 right parenthesis to the power of 4 end root over denominator negative 2 left parenthesis 0 right parenthesis minus 2 left parenthesis 0 right parenthesis squared end fraction close parentheses end cell row blank equals cell 1 over 0 end cell end table$

Hasil dari limit tersebut adalah tidak terdefinisi.