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Pertanyaan

begin mathsize 14px style limit as x rightwards arrow 5 of invisible function application fraction numerator 3 minus square root of x plus 4 end root over denominator x minus 5 end fraction equals... end style 

  1. begin mathsize 14px style 6 end style 

  2. begin mathsize 14px style 1 end style 

  3. begin mathsize 14px style 1 over 6 end style 

  4. begin mathsize 14px style 0 end style  

  5. begin mathsize 14px style negative 1 over 6 end style 

A. Damanhuri

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Jika dijumpai limit dengan bentuk akar dan tidak dapat difaktorkan secara langsung, maka kalikan dengan bentuk sekawannya.

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 5 of invisible function application fraction numerator 3 minus square root of x plus 4 end root over denominator x minus 5 end fraction end cell equals cell limit as x rightwards arrow 5 of invisible function application fraction numerator 3 minus square root of x plus 4 end root over denominator x minus 5 end fraction times fraction numerator 3 plus square root of x plus 4 end root over denominator 3 plus square root of x plus 4 end root end fraction end cell row blank equals cell limit as x rightwards arrow 5 of space fraction numerator 9 minus left parenthesis x plus 4 right parenthesis over denominator left parenthesis x minus 5 right parenthesis open parentheses 3 plus square root of x plus 4 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 5 of space fraction numerator 5 minus x over denominator left parenthesis x minus 5 right parenthesis left parenthesis 3 plus square root of x plus 4 end root right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 5 of fraction numerator negative up diagonal strike left parenthesis x minus 5 right parenthesis end strike over denominator up diagonal strike left parenthesis x minus 5 right parenthesis end strike open parentheses 3 plus square root of x plus 4 end root close parentheses end fraction end cell row blank equals cell fraction numerator negative 1 over denominator 3 plus square root of 5 plus 4 end root end fraction end cell row blank equals cell fraction numerator negative 1 over denominator 3 plus square root of 9 end fraction end cell row blank equals cell negative 1 over 6 end cell end table end style

Dengan demikian, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 5 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 minus square root of x plus 4 end root over denominator x minus 5 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 6 end cell end table end style.

Jadi, jawaban yang tepat adalah E.

10

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