Roboguru

Diketahui .

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals square root of 2 x plus 1 end root end style

begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator f open parentheses x plus 1 close parentheses minus f open parentheses 1 minus x close parentheses over denominator x end fraction equals... end style 

  1. begin mathsize 14px style negative 2 over 3 square root of 3 end style 

  2. begin mathsize 14px style 2 over 3 square root of 3 end style 

  3. begin mathsize 14px style square root of 3 end style 

  4. begin mathsize 14px style 2 square root of 3 end style 

  5. begin mathsize 14px style 6 square root of 3 end style 

Jawaban:

begin mathsize 14px style f open parentheses x close parentheses equals square root of 2 x plus 1 end root end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x plus 1 close parentheses end cell equals cell square root of 2 open parentheses x plus 1 close parentheses plus 1 end root end cell row blank equals cell square root of 2 x plus 2 plus 1 end root end cell row blank equals cell square root of 2 x plus 3 end root end cell row blank blank blank row cell f open parentheses 1 minus x close parentheses end cell equals cell square root of 2 open parentheses 1 minus x close parentheses plus 1 end root end cell row blank equals cell square root of 2 minus 2 x plus 1 end root end cell row blank equals cell square root of 3 minus 2 x end root end cell end table end style 

Sehingga 

begin mathsize 11px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator f left parenthesis x plus 1 right parenthesis minus f left parenthesis 1 minus x right parenthesis over denominator x end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator square root of 2 x plus 3 end root minus square root of 3 minus 2 x end root over denominator x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of open parentheses fraction numerator square root of 2 x plus 3 end root minus square root of 3 minus 2 x end root over denominator x end fraction close parentheses times open parentheses fraction numerator square root of 2 x plus 3 end root plus square root of 3 minus 2 x end root over denominator square root of 2 x plus 3 end root plus square root of 3 minus 2 x end root end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator open parentheses square root of 2 x plus 3 end root minus square root of 3 minus 2 x end root close parentheses open parentheses square root of 2 x plus 3 end root plus square root of 3 minus 2 x end root close parentheses over denominator x open parentheses square root of 2 x plus 3 end root plus square root of 3 minus 2 x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator open parentheses 2 x plus 3 close parentheses minus open parentheses 3 minus 2 x close parentheses over denominator x open parentheses square root of 2 x plus 3 end root plus square root of 3 minus 2 x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 4 x over denominator x open parentheses square root of 2 x plus 3 end root plus square root of 3 minus 2 x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 4 over denominator square root of 2 x plus 3 end root plus square root of 3 minus 2 x end root end fraction end cell row blank equals cell fraction numerator 4 over denominator square root of 2 open parentheses 0 close parentheses plus 3 end root plus square root of 3 minus 2 open parentheses 0 close parentheses end root end fraction end cell row blank equals cell fraction numerator 4 over denominator square root of 3 plus square root of 3 end fraction end cell row blank equals cell fraction numerator 4 over denominator 2 square root of 3 end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 3 end fraction end cell row blank equals cell 2 over 3 square root of 3 end cell end table end style 

Jadi jawaban yang tepat adalah B.

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