Pertanyaan

x → 0 lim 5 − 5 − x 2 x = ....

$x \to 0 lim \frac{2 x}{5 - 5 - x} = ....$

K. Prameswari

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

nilai limit di atas adalah

Pembahasan

Menggunakan metode mengalikan dengan akar sekawan, dapat diperoleh Jadi, nilai limit di atas adalah

Menggunakan metode mengalikan dengan akar sekawan, dapat diperoleh

$begin mathsize 11px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator 2 x over denominator square root of 5 minus square root of 5 minus x end root end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator 2 x over denominator square root of 5 minus square root of 5 minus x end root end fraction cross times fraction numerator square root of 5 plus square root of 5 minus x end root over denominator square root of 5 plus square root of 5 minus x end root end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 2 x cross times open parentheses square root of 5 plus square root of 5 minus x end root close parentheses over denominator 5 minus open parentheses 5 minus x close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 2 x cross times open parentheses square root of 5 plus square root of 5 minus x end root close parentheses over denominator 5 minus 5 plus x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 2 x cross times open parentheses square root of 5 plus square root of 5 minus x end root close parentheses over denominator x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of open parentheses 2 cross times open parentheses square root of 5 plus square root of 5 minus x end root close parentheses close parentheses end cell row blank equals cell 2 cross times open parentheses square root of 5 plus square root of 5 minus 0 end root close parentheses end cell row blank equals cell 2 cross times open parentheses square root of 5 plus square root of 5 close parentheses end cell row blank equals cell 2 cross times 2 square root of 5 end cell row blank equals cell 4 square root of 5 end cell end table end style$

Jadi, nilai limit di atas adalah