Pertanyaan

Nilai x → 0 lim 3 − 9 + x 5 x adalah ....

Nilai $x \to 0 lim \frac{5 x}{3 - 9 + x}$ adalah ....

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N. Puspita

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Substitusi x = 0: Karena merupakan bentuk tak tentu, maka penyelesaiannya dengan metode mengalikan akar sekawan: (ingat: ) Jadi, jawaban yang tepat adalah A.

Substitusi x = 0:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of space fraction numerator 5 x over denominator 3 minus square root of 9 plus x end root end fraction end cell equals cell fraction numerator 5 times 0 over denominator 3 minus square root of 9 plus 0 end root end fraction end cell row blank equals cell 0 over 0 space left parenthesis tak space tentu right parenthesis end cell end table$

Karena 0 over 0 merupakan bentuk tak tentu, maka penyelesaiannya dengan metode mengalikan akar sekawan: (ingat: open parentheses a plus b close parentheses open parentheses a minus b close parentheses equals a squared minus b squared )

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of space fraction numerator 5 x over denominator 3 minus square root of 9 plus x end root end fraction end cell row blank equals cell limit as x rightwards arrow 0 of space fraction numerator 5 x over denominator 3 minus square root of 9 plus x end root end fraction cross times fraction numerator 3 plus square root of 9 plus x end root over denominator 3 plus square root of 9 plus x end root end fraction end cell row blank equals cell limit as x rightwards arrow 0 of space fraction numerator 5 x open parentheses 3 plus square root of 9 plus x end root close parentheses over denominator 3 squared minus open parentheses square root of 9 plus x end root close parentheses squared end fraction end cell row blank equals cell limit as x rightwards arrow 0 of space fraction numerator 5 x open parentheses 3 plus square root of 9 plus x end root close parentheses over denominator 9 minus open parentheses 9 plus x close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of space fraction numerator 5 x open parentheses 3 plus square root of 9 plus x end root close parentheses over denominator negative x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of space minus 5 times open parentheses 3 plus square root of 9 plus x end root close parentheses end cell row blank equals cell negative 5 times open parentheses 3 plus square root of 9 plus 0 end root close parentheses end cell row blank equals cell negative 5 times open parentheses 3 plus 3 close parentheses end cell row blank equals cell negative 5 times 6 end cell row blank equals cell negative 30 end cell end table$

Jadi, jawaban yang tepat adalah A.