Pertanyaan

Tentukan x → 0 lim 2 − 4 − x x .

Tentukan $x \to 0 lim \frac{x}{2 - 4 - x}$ . $\;$

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Habis dalam

Klaim

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x over denominator 2 minus square root of 4 minus x end root end fraction end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table$ .

Pembahasan

Dengan substitusi langsung: Dengan mengalikan bentuk sekawan: Bentuk mempunyai bentuk sekawan . Jadi, .

Dengan substitusi langsung:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator x over denominator 2 minus square root of 4 minus x end root end fraction end cell equals cell fraction numerator 0 over denominator 2 minus square root of 4 minus 0 end root end fraction end cell row blank equals cell fraction numerator 0 over denominator 2 minus 2 end fraction end cell row blank equals cell 0 over 0 space open parentheses tak space tentu close parentheses end cell end table$

Dengan mengalikan bentuk sekawan:

Bentuk 2 minus square root of 4 minus x end root mempunyai bentuk sekawan 2 plus square root of 4 minus x end root .

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

Jadi, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x over denominator 2 minus square root of 4 minus x end root end fraction end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table$ .