Pertanyaan

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

Nilai dari

$x \to \infty lim 4 x^{2} - 4 x + 3 - 4 x^{2} + 4 x + 3$

adalah ....

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Langkah pertama dalam menyelesaikan limit tak hingga bentuk akar adalah dengan mengalikan akar sekawan. Selanjutnya, membagi semua suku pembilang dan penyebut dengan variabel yang memiliki pangkat tertinggi. Maka diperoleh: Jadi, nilai dari adalah .

Langkah pertama dalam menyelesaikan limit tak hingga bentuk akar adalah dengan mengalikan akar sekawan. Selanjutnya, membagi semua suku pembilang dan penyebut dengan variabel yang memiliki pangkat tertinggi. Maka diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell size 12px lim with size 12px x size 12px rightwards arrow size 12px infinity below size 12px space square root of size 12px 4 size 12px x to the power of size 12px 2 size 12px minus size 12px 4 size 12px x size 12px plus size 12px 3 end root size 12px minus square root of size 12px 4 size 12px x to the power of size 12px 2 size 12px plus size 12px 4 size 12px x size 12px plus size 12px 3 end root end cell row blank size 12px equals cell size 12px lim with size 12px x size 12px rightwards arrow size 12px infinity below size 12px space square root of size 12px 4 size 12px x to the power of size 12px 2 size 12px minus size 12px 4 size 12px x size 12px plus size 12px 3 end root size 12px minus square root of size 12px 4 size 12px x to the power of size 12px 2 size 12px plus size 12px 4 size 12px x size 12px plus size 12px 3 end root size 12px cross times end cell row blank blank cell fraction numerator square root of size 12px 4 size 12px x to the power of size 12px 2 size 12px minus size 12px 4 size 12px x size 12px plus size 12px 3 end root size 12px plus square root of size 12px 4 size 12px x to the power of size 12px 2 size 12px plus size 12px 4 size 12px x size 12px plus size 12px 3 end root over denominator square root of size 12px 4 size 12px x to the power of size 12px 2 size 12px minus size 12px 4 size 12px x size 12px plus size 12px 3 end root size 12px plus square root of size 12px 4 size 12px x to the power of size 12px 2 size 12px plus size 12px 4 size 12px x size 12px plus size 12px 3 end root end fraction end cell row blank size 12px equals cell size 12px lim with size 12px x size 12px rightwards arrow size 12px infinity below size 12px space fraction numerator begin mathsize 12px style left parenthesis square root of 4 x squared minus 4 x plus 3 end root right parenthesis end style to the power of size 12px 2 size 12px minus begin mathsize 12px style left parenthesis square root of 4 x squared plus 4 x plus 3 end root right parenthesis end style to the power of size 12px 2 over denominator square root of size 12px 4 size 12px x to the power of size 12px 2 size 12px minus size 12px 4 size 12px x size 12px plus size 12px 3 end root size 12px plus square root of size 12px 4 size 12px x to the power of size 12px 2 size 12px plus size 12px 4 size 12px x size 12px plus size 12px 3 end root end fraction end cell row blank size 12px equals cell size 12px lim with size 12px x size 12px rightwards arrow size 12px infinity below size 12px space fraction numerator begin mathsize 12px style left parenthesis 4 x squared minus 4 x plus 3 right parenthesis end style size 12px minus begin mathsize 12px style left parenthesis 4 x squared plus 4 x plus 3 right parenthesis end style over denominator square root of size 12px 4 size 12px x to the power of size 12px 2 size 12px minus size 12px 4 size 12px x size 12px plus size 12px 3 end root size 12px plus square root of size 12px 4 size 12px x to the power of size 12px 2 size 12px plus size 12px 4 size 12px x size 12px plus size 12px 3 end root end fraction end cell row blank size 12px equals cell size 12px lim with size 12px x size 12px rightwards arrow size 12px infinity below size 12px space fraction numerator size 12px minus size 12px 8 size 12px x over denominator square root of size 12px 4 size 12px x to the power of size 12px 2 size 12px minus size 12px 4 size 12px x size 12px plus size 12px 3 end root size 12px plus square root of size 12px 4 size 12px x to the power of size 12px 2 size 12px plus size 12px 4 size 12px x size 12px plus size 12px 3 end root end fraction end cell row blank size 12px equals cell size 12px lim with size 12px x size 12px rightwards arrow size 12px infinity below size 12px space fraction numerator begin mathsize 12px display style fraction numerator negative 8 x over denominator x end fraction end style over denominator square root of begin mathsize 12px display style fraction numerator 4 x squared over denominator x squared end fraction minus fraction numerator 4 x over denominator x squared end fraction plus 3 over x squared end style end root size 12px plus square root of begin mathsize 12px display style fraction numerator 4 x squared over denominator x squared end fraction plus fraction numerator 4 x over denominator x squared end fraction plus 3 over x squared end style end root size 12px space end fraction end cell row blank size 12px equals cell size 12px lim with size 12px x size 12px rightwards arrow size 12px infinity below size 12px space fraction numerator begin mathsize 12px display style negative 8 end style over denominator square root of begin mathsize 12px display style 4 minus 4 over x plus 3 over x squared end style end root size 12px plus square root of begin mathsize 12px display style 4 plus 4 over x plus 3 over x squared end style end root size 12px space end fraction end cell row blank size 12px equals cell fraction numerator size 12px minus size 12px 8 over denominator square root of size 12px 4 size 12px minus size 12px 0 size 12px plus size 12px 0 end root size 12px plus square root of size 12px 4 size 12px plus size 12px 0 size 12px plus size 12px 0 end root end fraction end cell row blank size 12px equals cell fraction numerator size 12px minus size 12px 8 over denominator square root of size 12px 4 size 12px plus square root of size 12px 4 end fraction end cell row blank size 12px equals cell fraction numerator size 12px minus size 12px 8 over denominator size 12px 2 size 12px plus size 12px 2 end fraction end cell row blank size 12px equals cell fraction numerator size 12px minus size 12px 8 over denominator size 12px 4 end fraction end cell row blank size 12px equals cell size 12px minus size 12px 2 end cell end table$

Jadi, nilai dari

limit as x rightwards arrow infinity of space square root of 4 x squared minus 4 x plus 3 end root minus square root of 4 x squared plus 4 x plus 3 end root

adalah negative 2 .

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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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