Pertanyaan

Nilai dari x → 3 lim 3 x 2 − 2 − 5 x 2 − x − 6 = ...

Nilai dari $x \to 3 lim \frac{x ^{2} - x - 6}{3 x ^{2} - 2 - 5} = ...$

F. Faiz

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari $limit as x rightwards arrow 3 of fraction numerator x squared minus x minus 6 over denominator square root of 3 x squared minus 2 end root minus 5 end fraction$ adalah 25 over 9

Pembahasan

Jadi, nilai dari adalah .

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 3 of fraction numerator x squared minus x minus 6 over denominator square root of 3 x squared minus 2 end root minus 5 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator x squared minus x minus 6 over denominator square root of 3 x squared minus 2 end root minus 5 end fraction cross times fraction numerator square root of 3 x squared minus 2 end root plus 5 over denominator square root of 3 x squared minus 2 end root plus 5 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses x squared minus x minus 6 close parentheses open parentheses square root of 3 x squared minus 2 end root plus 5 close parentheses over denominator open parentheses 3 x squared minus 2 close parentheses minus 25 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses x squared minus x minus 6 close parentheses open parentheses square root of 3 x squared minus 2 end root plus 5 close parentheses over denominator 3 x squared minus 27 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator up diagonal strike open parentheses x minus 3 close parentheses end strike open parentheses x plus 2 close parentheses open parentheses square root of 3 x squared minus 2 end root plus 5 close parentheses over denominator 3 up diagonal strike left parenthesis x minus 3 right parenthesis end strike left parenthesis x plus 3 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses x plus 2 close parentheses open parentheses square root of 3 x squared minus 2 end root plus 5 close parentheses over denominator 3 left parenthesis x plus 3 right parenthesis end fraction end cell row blank equals cell fraction numerator open parentheses 3 plus 2 close parentheses open parentheses square root of 3 left parenthesis 3 right parenthesis squared minus 2 end root plus 5 close parentheses over denominator 3 left parenthesis 3 plus 3 right parenthesis end fraction end cell row blank equals cell fraction numerator 5 open parentheses square root of 3 open parentheses 9 close parentheses minus 2 end root plus 5 close parentheses over denominator 3 left parenthesis 6 right parenthesis end fraction end cell row blank equals cell fraction numerator 5 open parentheses square root of 27 minus 2 end root plus 5 close parentheses over denominator 3 left parenthesis 6 right parenthesis end fraction end cell row blank equals cell fraction numerator 5 open parentheses square root of 25 plus 5 close parentheses over denominator 3 left parenthesis 6 right parenthesis end fraction end cell row blank equals cell fraction numerator 5 open parentheses 5 plus 5 close parentheses over denominator 3 left parenthesis 6 right parenthesis end fraction end cell row blank equals cell fraction numerator 5 open parentheses 10 close parentheses over denominator 3 left parenthesis 6 right parenthesis end fraction end cell row blank equals cell 50 over 18 end cell row blank equals cell 25 over 9 end cell row blank blank blank end table$

Jadi, nilai dari $limit as x rightwards arrow 3 of fraction numerator x squared minus x minus 6 over denominator square root of 3 x squared minus 2 end root minus 5 end fraction$ adalah 25 over 9 .