Pertanyaan

x → ∞ lim x 2 − 2 x + 1 x + 1 = ...

$x \to \infty lim \frac{x + 1}{x ^{2} - 2 x + 1} = ...$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

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$begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator x plus 1 over denominator x squared minus 2 x plus 1 end fraction equals space 0 end style$ .

Pembahasan

Dengan mengalikan pembilang dan penyebut dengan diperoleh Jadi .

$begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator x plus 1 over denominator x squared minus 2 x plus 1 end fraction end style$

Dengan mengalikan pembilang dan penyebut dengan diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator x plus 1 over denominator x squared minus 2 x plus 1 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator x plus 1 over denominator x squared minus 2 x plus 1 end fraction cross times fraction numerator begin display style 1 over x squared end style over denominator begin display style 1 over x squared end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 1 over x end style plus begin display style 1 over x squared end style over denominator 1 minus begin display style 2 over x end style plus begin display style 1 over x squared end style end fraction end cell row blank equals cell fraction numerator 0 plus 0 over denominator 1 minus 0 plus 0 end fraction end cell row blank equals cell 0 over 1 end cell row blank equals 0 end table end style$

Jadi $begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator x plus 1 over denominator x squared minus 2 x plus 1 end fraction equals space 0 end style$ .