Pertanyaan

Tentukan nilai dari x → 0 lim x 2 + x − 2 − x

Tentukan nilai dari $x \to 0 lim \frac{2 + x - 2 - x}{x}$

H. Firmansyah

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Pembahasan

Subtitusi nilai x : Karena hasil merupakan bentuk tak tentu, maka difaktorkan sebagai berikut: Jadi, .

Subtitusi nilai x:

Karena hasil merupakan bentuk tak tentu, maka difaktorkan sebagai berikut:

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

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