Pertanyaan

Tentukan nilai: x → 0 lim x 2 − x 1 − x + 1

Tentukan nilai:

$x \to 0 lim \frac{1 - x + 1}{x ^{2} - x}$

R. RGFLLIMA

Master Teacher

Jawaban terverifikasi

Jawaban

Nilai

Nilai $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 minus square root of straight x plus 1 end root over denominator straight x squared minus straight x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table end style$

Pembahasan

Mensubstitusikan nilai maka diperoleh: Karena hasilnyabentuk tak tentu yaitu maka dilanjutkan dengan menerapkan metode perkalian sekawan, Jadi, Nilai

Mensubstitusikan nilai begin mathsize 14px style straight x equals 0 end style maka diperoleh:

Karena hasilnya bentuk tak tentu yaitu begin mathsize 14px style 0 over 0 end style maka dilanjutkan dengan menerapkan metode perkalian sekawan,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow 0 of fraction numerator 1 minus square root of straight x plus 1 end root over denominator straight x squared minus straight x end fraction end cell equals cell limit as straight x rightwards arrow 0 of fraction numerator left parenthesis 1 minus square root of straight x plus 1 end root right parenthesis over denominator left parenthesis straight x squared minus straight x right parenthesis end fraction times fraction numerator left parenthesis 1 plus square root of straight x plus 1 end root right parenthesis over denominator left parenthesis 1 plus square root of straight x plus 1 end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 0 of fraction numerator left parenthesis 1 minus left parenthesis straight x plus 1 right parenthesis over denominator left parenthesis straight x squared minus straight x right parenthesis left parenthesis 1 plus square root of straight x plus 1 end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 0 of fraction numerator 1 minus straight x minus 1 over denominator left parenthesis straight x squared minus straight x right parenthesis left parenthesis 1 plus square root of straight x plus 1 end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 0 of fraction numerator negative straight x over denominator straight x left parenthesis straight x minus 1 right parenthesis left parenthesis 1 plus square root of straight x plus 1 end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 0 of fraction numerator negative 1 over denominator 1 left parenthesis straight x minus 1 right parenthesis left parenthesis 1 plus square root of straight x plus 1 end root right parenthesis end fraction end cell row blank equals cell fraction numerator negative 1 over denominator 1 left parenthesis 0 minus 1 right parenthesis left parenthesis 1 plus square root of 0 plus 1 end root right parenthesis end fraction end cell row blank equals cell fraction numerator negative 1 over denominator left parenthesis negative 1 right parenthesis left parenthesis 1 plus square root of 1 right parenthesis end fraction end cell row blank equals cell fraction numerator negative 1 over denominator negative 1 left parenthesis 2 right parenthesis end fraction end cell row blank equals cell 1 half end cell end table end style$

Jadi, Nilai $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 minus square root of straight x plus 1 end root over denominator straight x squared minus straight x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table end style$