Pertanyaan

Nilai dari x → ∞ lim ( 4 x 2 + 3 x + 4 − 6 x 2 − 4 x + 1 ) = …

Nilai dari $x \to \infty lim (4 x^{2} + 3 x + 4 - 6 x^{2} - 4 x + 1)$ = $\dots$

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nilai adalah

nilai

adalah

Pembahasan

penyelesaian limit tak hingga dengan cara berikut. Jadi, nilai adalah

penyelesaian limit tak hingga dengan cara berikut.

$space limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 3 x plus 4 end root minus square root of 6 x squared minus 4 x plus 1 end root close parentheses times fraction numerator square root of 4 x squared plus 3 x plus 4 end root plus square root of 6 x squared minus 4 x plus 1 end root over denominator square root of 4 x squared plus 3 x plus 4 end root plus square root of 6 x squared minus 4 x plus 1 end root end fraction left right double arrow limit as x rightwards arrow infinity of fraction numerator open parentheses 4 x squared plus 3 x plus 4 close parentheses minus open parentheses 6 x squared minus 4 x plus 1 close parentheses over denominator square root of 4 x squared plus 3 x plus 4 end root plus square root of 6 x squared minus 4 x plus 1 end root end fraction left right double arrow limit as x rightwards arrow infinity of fraction numerator negative 2 x squared plus 7 x plus 3 over denominator square root of 4 x squared plus 3 x plus 4 end root plus square root of 6 x squared minus 4 x plus 1 end root end fraction left right double arrow limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator negative 2 x squared over denominator x squared end fraction end style plus begin display style fraction numerator 7 x over denominator x squared end fraction end style plus begin display style 3 over x squared end style over denominator square root of begin display style fraction numerator 4 x squared over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 3 x over denominator x to the power of 4 end fraction end style plus begin display style 4 over x to the power of 4 end style end root plus square root of begin display style fraction numerator 6 x squared over denominator x to the power of 4 end fraction end style minus begin display style fraction numerator 4 x over denominator x to the power of 4 end fraction end style plus begin display style 1 over x to the power of 4 end style end root end fraction left right double arrow limit as x rightwards arrow infinity of fraction numerator begin display style negative 2 plus 7 over x plus 3 over x squared end style over denominator square root of begin display style 4 over x squared plus 3 over x cubed plus 4 over x to the power of 4 end style end root plus square root of begin display style 6 over x squared minus 4 over x cubed plus 1 over x to the power of 4 end style end root end fraction left right double arrow fraction numerator begin display style negative 2 plus 7 over infinity plus 3 over infinity squared end style over denominator square root of begin display style 4 over infinity squared plus 3 over infinity cubed plus 4 over infinity to the power of 4 end style end root plus square root of begin display style 6 over infinity squared minus 4 over infinity cubed plus 1 over infinity to the power of 4 end style end root end fraction left right double arrow fraction numerator negative 2 plus 0 plus 0 over denominator square root of 0 plus square root of 0 end fraction left right double arrow left right double arrow fraction numerator negative 2 over denominator 0 end fraction equals negative infinity$

Jadi, nilai adalah

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$\style{font-size:14px}{\mathrm{Nilai}}\style{font-size:14px}\;\underset{\style{font-size:14px}{\mathrm x}\style{font-size:14px}\rightarrow\style{font-size:14px}\infty}{\style{font-size:14px}\lim}\left(\sqrt{\style{font-size:14px}4\style{font-size:14px}{\mathrm x}^\style{font-size:14px}2\style{font-size:14px}\;\style{font-size:14px}+\style{font-size:14px}\;\style{font-size:14px}3\style{font-size:14px}{\mathrm x}\style{font-size:14px}\;\style{font-size:14px}+\style{font-size:14px}\;\style{font-size:14px}4}\style{font-size:14px}\;\style{font-size:14px}-\style{font-size:14px}\;\style{font-size:14px}2\style{font-size:14px}{\mathrm x}\style{font-size:14px}\;\style{font-size:14px}+\style{font-size:14px}1\right)\style{font-size:14px}\;\style{font-size:14px}=\style{font-size:14px}\;\style{font-size:14px}.\style{font-size:14px}.\style{font-size:14px}.\style{font-size:14px}.$

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