Pertanyaan

Hitunglah nilai dari x → 1 lim 2 − x + 3 x 2 − 2 x + 1 !

Hitunglah nilai dari $x \to 1 lim \frac{x ^{2} - 2 x + 1}{2 - x + 3}$ !

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

nilai dari adalah 0.

nilai dari $limit as x rightwards arrow 1 of fraction numerator x squared minus 2 x plus 1 over denominator 2 minus square root of x plus 3 end root end fraction$ adalah 0.

Pembahasan

Jadi, nilai dari adalah 0.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of fraction numerator x squared minus 2 x plus 1 over denominator 2 minus square root of x plus 3 end root end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator x squared minus 2 x plus 1 over denominator 2 minus square root of x plus 3 end root end fraction times fraction numerator 2 plus square root of x plus 3 end root over denominator 2 plus square root of x plus 3 end root end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator left parenthesis x squared minus 2 x plus 1 right parenthesis left parenthesis 2 plus square root of x plus 3 end root right parenthesis over denominator 4 minus left parenthesis x plus 3 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator left parenthesis x minus 1 right parenthesis left parenthesis x minus 1 right parenthesis left parenthesis 2 plus square root of x plus 3 end root right parenthesis over denominator negative x plus 1 end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator left parenthesis x minus 1 right parenthesis left parenthesis x minus 1 right parenthesis left parenthesis 2 plus square root of x plus 3 end root right parenthesis over denominator negative left parenthesis x minus 1 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 1 of minus left parenthesis x minus 1 right parenthesis left parenthesis 2 plus square root of x plus 3 end root right parenthesis end cell row blank equals cell negative left parenthesis 1 minus 1 right parenthesis left parenthesis 2 plus square root of 1 plus 3 end root right parenthesis end cell row blank equals cell negative left parenthesis 0 right parenthesis left parenthesis 4 right parenthesis end cell row blank equals 0 end table$

Jadi, nilai dari $limit as x rightwards arrow 1 of fraction numerator x squared minus 2 x plus 1 over denominator 2 minus square root of x plus 3 end root end fraction$ adalah 0.