Pertanyaan

Nilai dari x → ∞ lim ( x + 2 ) ( x − 3 ) 3 x 4 − 2 x 2 + x adalah ....

Nilai dari $x \to \infty lim \frac{3 x ^{4} - 2 x ^{2} + x}{( x + 2 ) ( x - 3 )}$ adalah ....

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Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari $begin mathsize 14px style limit as straight x rightwards arrow infinity of fraction numerator 3 straight x to the power of 4 minus 2 straight x squared plus straight x over denominator left parenthesis straight x plus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction end style$ adalah

Pembahasan

Ingat: . = = = = = = = = lim x → ∞ ( x + 2 ) ( x − 3 ) 3 x 4 − 2 x 2 + x lim x → ∞ x 2 − x − 6 3 x 4 − 2 x 2 + x lim x → ∞ x 2 − x − 6 3 x 4 − 2 x 2 + x × x 4 1 x 4 1 lim x → ∞ x 4 x 2 − x 4 x − x 4 6 x 4 3 x 4 − x 4 2 x 2 + x 4 x lim x → ∞ x 2 1 − x 3 1 − x 4 6 3 − x 2 2 + x 3 1 ∞ 2 1 − ∞ 3 1 − ∞ 4 6 3 − ∞ 2 2 + ∞ 3 1 0 − 0 − 0 3 − 0 + 0 0 3 ∞ Dengan demikian, nilai dari adalah .

Ingat: limit as x rightwards arrow infinity of k over x to the power of n equals k over infinity to the power of n equals 0 .

$= = = = = = = = lim_{x \to \infty} \frac{3 x ^{4} - 2 x ^{2} + x}{( x + 2 ) ( x - 3 )} lim_{x \to \infty} \frac{3 x ^{4} - 2 x ^{2} + x}{x ^{2} - x - 6} lim_{x \to \infty} \frac{3 x ^{4} - 2 x ^{2} + x}{x ^{2} - x - 6} \times \frac{\frac{1}{x ^{4}}}{\frac{1}{x ^{4}}} lim_{x \to \infty} \frac{\frac{3 x ^{4}}{x ^{4}} - \frac{2 x ^{2}}{x ^{4}} + \frac{x}{x ^{4}}}{\frac{x ^{2}}{x ^{4}} - \frac{x}{x ^{4}} - \frac{6}{x ^{4}}} lim_{x \to \infty} \frac{3 - \frac{2}{x ^{2}} + \frac{1}{x ^{3}}}{\frac{1}{x ^{2}} - \frac{1}{x ^{3}} - \frac{6}{x ^{4}}} \frac{3 - \frac{2}{\infty ^{2}} + \frac{1}{\infty ^{3}}}{\frac{1}{\infty ^{2}} - \frac{1}{\infty ^{3}} - \frac{6}{\infty ^{4}}} \frac{3 - 0 + 0}{0 - 0 - 0} \frac{3}{0} \infty$

Dengan demikian, nilai dari $begin mathsize 14px style limit as straight x rightwards arrow infinity of fraction numerator 3 straight x to the power of 4 minus 2 straight x squared plus straight x over denominator left parenthesis straight x plus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction end style$ adalah .