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Diketahui f(x)=x4−a4x2−a2​, a=0. Nilai x→alim​f(x)=....

Pertanyaan

Diketahui f left parenthesis x right parenthesis equals fraction numerator x squared minus a squared over denominator x to the power of 4 minus a to the power of 4 end fraction comma space a not equal to 0. Nilai limit as x rightwards arrow a of f left parenthesis x right parenthesis equals....

  1. begin mathsize 14px style 1 over a squared end style 

  2. begin mathsize 14px style fraction numerator 1 over denominator 2 a squared end fraction end style 

  3. begin mathsize 14px style fraction numerator 1 over denominator 3 a squared end fraction end style 

  4. begin mathsize 14px style fraction numerator 1 over denominator 4 a squared end fraction end style 

  5. begin mathsize 14px style fraction numerator 1 over denominator 6 a squared end fraction end style  

S. Dwi

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator x squared minus a squared over denominator x to the power of 4 minus a to the power of 4 end fraction comma space a not equal to 0 end style, maka nilai limitnya sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow a of f open parentheses x close parentheses end cell equals cell limit as x rightwards arrow a of space fraction numerator x squared minus a squared over denominator x to the power of 4 minus a to the power of 4 end fraction end cell row blank equals cell fraction numerator a squared minus a squared over denominator a to the power of 4 minus a to the power of 4 end fraction end cell row blank equals cell 0 over 0 end cell end table

Karena diperoleh nilai 0 over 0, maka kerjakan dengan metode pemfaktoran.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow a of f open parentheses x close parentheses end cell equals cell limit as x rightwards arrow a of fraction numerator x squared minus a squared over denominator x to the power of 4 minus a to the power of 4 end fraction end cell row blank equals cell limit as x rightwards arrow a of fraction numerator x squared minus a squared over denominator open parentheses x squared minus a squared close parentheses open parentheses x squared plus a squared close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow a of fraction numerator up diagonal strike x squared minus a squared end strike over denominator up diagonal strike open parentheses x squared minus a squared close parentheses end strike open parentheses x squared plus a squared close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow a of fraction numerator 1 over denominator x squared plus a squared end fraction end cell row blank equals cell fraction numerator 1 over denominator a squared plus a squared end fraction end cell row blank equals cell fraction numerator 1 over denominator 2 a squared end fraction end cell end table end style 

Oleh karena itu, jawaban yang tepat adalah B.

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