Roboguru

Nilai dari

Nilai dari limit as x rightwards arrow infinity of square root of 5 x squared plus 3 x end root minus square root of 4 x squared minus 2 end root equals... 

Jawaban:

table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell limit as x rightwards arrow infinity of square root of 5 x squared plus 3 x end root minus square root of 4 x squared minus 2 end root cross times fraction numerator square root of 5 x squared plus 3 x end root plus square root of 4 x squared minus 2 end root over denominator square root of 5 x squared plus 3 x end root plus square root of 4 x squared minus 2 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses 5 x squared plus 3 x close parentheses minus open parentheses 4 x squared minus 2 close parentheses over denominator square root of 5 x squared plus 3 x end root plus square root of 4 x squared minus 2 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 5 x squared plus 3 x minus 4 x squared plus 2 over denominator square root of 5 x squared plus 3 x end root plus square root of 4 x squared minus 2 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator x squared plus 3 x plus 2 over denominator square root of 5 x squared plus 3 x end root plus square root of 4 x squared minus 2 end root end fraction cross times fraction numerator begin display style 1 over x squared end style over denominator begin display style 1 over x squared end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style x squared over x squared end style plus begin display style fraction numerator 3 x over denominator x squared end fraction end style plus begin display style 2 over x squared end style over denominator square root of begin display style fraction numerator 5 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 end root plus square root of begin display style fraction numerator 4 x squared over denominator x to the power of 4 end fraction end style minus begin display style 2 over x to the power of 4 end style end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 1 plus begin display style 3 over x end style plus 2 over x squared over denominator square root of 5 over x squared plus 3 over x cubed end root plus square root of 4 over x squared minus 2 over x to the power of 4 end root end fraction end cell row blank equals cell fraction numerator 1 plus begin display style 3 over infinity end style plus 2 over infinity over denominator square root of 5 over infinity plus 3 over infinity end root plus square root of 4 over infinity minus 2 over infinity end root end fraction end cell row blank equals cell fraction numerator 1 plus 0 plus 0 over denominator 0 plus 0 plus 0 plus 0 end fraction end cell row blank equals infinity end table 

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