Pertanyaan

Hitunglah nilai dari x → 1 lim x 3 + 5 x 2 + 2 x − 12 x 3 + 27 .

Hitunglah nilai dari $x \to 1 lim \frac{x ^{3} + 27}{x ^{3} + 5 x ^{2} + 2 x - 12}$ .

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Jawaban terverifikasi

Jawaban

, .

, $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x cubed plus 27 over denominator x cubed plus 5 x squared plus 2 x minus 12 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 7 end table end style$ .

Pembahasan

Jadi , .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of fraction numerator x cubed plus 27 over denominator x cubed plus 5 x squared plus 2 x minus 12 end fraction end cell row blank equals cell fraction numerator limit as x rightwards arrow 1 of open parentheses x cubed plus 27 close parentheses over denominator limit as x rightwards arrow 1 of open parentheses x cubed plus 5 x squared plus 2 x minus 12 close parentheses end fraction end cell row blank equals cell fraction numerator limit as x rightwards arrow 1 of x cubed plus limit as x rightwards arrow 1 of 27 over denominator limit as x rightwards arrow 1 of x cubed plus 5 limit as x rightwards arrow 1 of x squared plus 2 limit as x rightwards arrow 1 of x minus limit as x rightwards arrow 1 of 12 end fraction end cell row blank equals cell fraction numerator 1 cubed plus 27 over denominator 1 cubed plus 5 times 1 squared plus 2 times 1 minus 12 end fraction end cell row blank equals cell fraction numerator 28 over denominator 1 plus 5 plus 2 minus 12 end fraction end cell row blank equals cell fraction numerator 28 over denominator negative 4 end fraction end cell row blank equals cell negative 7 end cell end table end style$

Jadi, $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x cubed plus 27 over denominator x cubed plus 5 x squared plus 2 x minus 12 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 7 end table end style$ .

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