Pertanyaan

x → 3 lim x 2 − 3 x x 2 + 3 x − 18

$x \to 3 lim \frac{x ^{2} + 3 x - 18}{x ^{2} - 3 x}$

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Jawaban terverifikasi

Jawaban

nilai adalah 3

nilai $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 3 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared plus 3 x minus 18 over denominator x squared minus 3 x end fraction end cell end table$ adalah 3

Pembahasan

substitusi nilai x = 3 Karena bentuk tak tentu, maka tidak boleh dan harus diselesaikan dengan cara pemfaktoran: Jadi, nilai adalah 3

substitusi nilai x = 3

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x squared plus 3 x minus 18 over denominator x squared minus 3 x end fraction end cell equals cell fraction numerator 3 squared plus 3 times 3 minus 18 over denominator 3 squared minus 3 times 3 end fraction end cell row blank equals cell fraction numerator 9 plus 9 minus 18 over denominator 9 minus 9 end fraction end cell row blank equals cell 0 over 0 space open parentheses tak space tentu close parentheses end cell end table$

Karena 0 over 0 bentuk tak tentu, maka tidak boleh dan harus diselesaikan dengan cara pemfaktoran:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x squared plus 3 x minus 18 over denominator x squared minus 3 x end fraction end cell equals cell limit as x rightwards arrow 3 of fraction numerator left parenthesis x plus 6 right parenthesis up diagonal strike left parenthesis x minus 3 right parenthesis end strike over denominator x up diagonal strike left parenthesis x minus 3 right parenthesis end strike end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator left parenthesis x plus 6 right parenthesis over denominator x end fraction end cell row blank equals cell fraction numerator 3 plus 6 over denominator 3 end fraction end cell row blank equals cell 9 over 3 end cell row blank equals 3 end table$

Jadi, nilai $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 3 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared plus 3 x minus 18 over denominator x squared minus 3 x end fraction end cell end table$ adalah 3