Pertanyaan

Tentukan nilai dari x → 0 lim 3 − 9 − x x

Tentukan nilai dari $x \to 0 lim \frac{x}{3 - 9 - x}$

J. Joko

Master Teacher

Jawaban terverifikasi

Jawaban

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$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x over denominator 3 minus square root of 9 minus x end root end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table 6 end style$ .

Pembahasan

Subtitusi nilai x : Karena hasil tidak terdefinisi, maka difaktorkan sebagai berikut: Jadi, .

Subtitusi nilai x:

Karena hasil tidak terdefinisi, maka difaktorkan sebagai berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator x over denominator 3 minus square root of 9 minus x end root end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator x over denominator 3 minus square root of 9 minus x end root end fraction times fraction numerator 3 plus square root of 9 minus x end root over denominator 3 plus square root of 9 minus x end root end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x left parenthesis 3 plus square root of 9 minus x end root right parenthesis over denominator 9 minus left parenthesis 9 minus x right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x left parenthesis 3 plus square root of 9 minus x end root right parenthesis over denominator x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of 3 plus square root of 9 minus x end root end cell row blank equals cell 3 plus square root of 9 minus 0 end root end cell row blank equals cell 3 plus 3 end cell row blank equals 6 end table end style$

Jadi, $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x over denominator 3 minus square root of 9 minus x end root end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table 6 end style$ .