Pertanyaan

x → 1 lim 1 − x 2 1 − x = …

$x \to 1 lim \frac{1 - x}{1 - x ^{2}} = \dots$

R. Bella

Master Teacher

Mahasiswa/Alumni UIN Syarif Hidayatullah Jakarta

Jawaban terverifikasi

Jawaban

diperoleh nilai .

diperoleh nilai $begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator 1 minus square root of x over denominator 1 minus x squared end fraction equals 1 fourth end style$ .

Pembahasan

Dengan mengalikan akar sekawan, diperoleh perhitungan sebagai berikut: Jadi, diperoleh nilai .

Dengan mengalikan akar sekawan, diperoleh perhitungan sebagai berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator 1 minus square root of x over denominator 1 minus x squared end fraction end cell equals cell limit as x rightwards arrow 1 of fraction numerator 1 minus square root of x over denominator 1 minus x squared end fraction cross times fraction numerator 1 plus square root of x over denominator 1 plus square root of x end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 1 minus x over denominator open parentheses 1 minus x squared close parentheses open parentheses 1 plus square root of x close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator up diagonal strike 1 minus x end strike over denominator up diagonal strike left parenthesis 1 minus x right parenthesis end strike left parenthesis 1 plus x right parenthesis open parentheses 1 plus square root of x close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 1 over denominator left parenthesis 1 plus x right parenthesis open parentheses 1 plus square root of x close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator left parenthesis 1 plus 1 right parenthesis left parenthesis 1 plus square root of 1 right parenthesis end fraction end cell row blank equals cell fraction numerator 1 over denominator 2 times 2 end fraction end cell row blank equals cell 1 fourth end cell end table end style$

Jadi, diperoleh nilai $begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator 1 minus square root of x over denominator 1 minus x squared end fraction equals 1 fourth end style$ .