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begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses 2 x plus 2 minus square root of 4 x squared minus x minus 4 end root close parentheses equals.... end style 

  1. begin mathsize 14px style 1 half end style 

  2. begin mathsize 14px style 7 over 4 end style 

  3. undefined 

  4. begin mathsize 14px style 9 over 4 end style 

  5. begin mathsize 14px style 9 over 2 end style 

Jawaban:

begin mathsize 11px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of open parentheses 2 x plus 2 minus square root of 4 x squared minus x minus 4 end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses 2 x plus 2 minus square root of 4 x squared minus x minus 4 end root close parentheses cross times open parentheses fraction numerator 2 x plus 2 plus square root of 4 x squared minus x minus 4 end root over denominator 2 x plus 2 plus square root of 4 x squared minus x minus 4 end root end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses 2 x plus 2 close parentheses squared minus open parentheses 4 x squared minus x minus 4 close parentheses over denominator 2 x plus 2 plus square root of 4 x squared minus x minus 4 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses 4 x squared plus 8 x plus 4 close parentheses minus open parentheses 4 x squared minus x minus 4 close parentheses over denominator 2 x plus 2 plus square root of x squared open parentheses 4 minus begin display style 1 over x end style minus begin display style 4 over x squared end style close parentheses end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 9 x plus 8 over denominator x open parentheses 2 plus begin display style 2 over x end style close parentheses plus x square root of 4 minus begin display style 1 over x end style minus begin display style 4 over x squared end style end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator x open parentheses 9 plus begin display style 8 over x end style close parentheses over denominator x open parentheses left parenthesis 2 plus 2 over x right parenthesis plus square root of 4 minus 1 over x minus 4 over x squared end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 9 plus 8 over x over denominator left parenthesis 2 plus 2 over x right parenthesis plus square root of 4 minus 1 over x minus 4 over x squared end root end fraction end cell row blank equals cell fraction numerator 9 plus 0 over denominator left parenthesis 2 plus 0 right parenthesis plus square root of 4 minus 0 minus 0 end root end fraction end cell row blank equals cell fraction numerator 9 over denominator 2 plus 2 end fraction end cell row blank equals cell 9 over 4 end cell end table end style 

Jadi, jawaban yang tepat adalah D.undefined 

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