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Pertanyaan

begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator x squared minus 2 x over denominator x squared minus 4 end fraction equals horizontal ellipsis end style  

  1. begin mathsize 14px style 0 end style 

  2. begin mathsize 14px style infinity end style 

  3. begin mathsize 14px style 1 half end style 

  4. begin mathsize 14px style 2 end style 

  5. begin mathsize 14px style negative 2 end style 

Pembahasan Soal:

Untuk begin mathsize 14px style x equals 2 end style maka

begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator x squared minus 2 x over denominator x squared minus 4 end fraction equals fraction numerator 2 squared minus 2 left parenthesis 2 right parenthesis over denominator 2 squared minus 4 end fraction equals equals fraction numerator 4 minus 4 over denominator 4 minus 4 end fraction equals 0 over 0 end style.  

Diperoleh nilai begin mathsize 14px style 0 over 0 end style. Oleh karena itu, harus difaktorkan terlebih dahulu,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator x squared minus 2 x over denominator x squared minus 4 end fraction end cell equals cell limit as x rightwards arrow 2 of fraction numerator x left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator x up diagonal strike left parenthesis x minus 2 right parenthesis end strike over denominator up diagonal strike left parenthesis x minus 2 right parenthesis end strike left parenthesis x plus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator x over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator 2 over denominator 2 plus 2 end fraction end cell row blank equals cell 2 over 4 end cell row blank equals cell 1 half end cell end table end style 

Dengan demikian, begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator x squared minus 2 x over denominator x squared minus 4 end fraction equals 1 half end style.

Jadi, jawaban yang tepat adalah C.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 13 Maret 2021

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