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Nilai dari: x→∞Lim​5x−3−25x2−10x+6​=...

Pertanyaan

Nilai dari:

stack L i m with x rightwards arrow infinity below 5 x minus 3 minus square root of 25 x squared minus 10 x plus 6 end root equals...

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell stack l i m with x rightwards arrow infinity below end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x 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 3 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 square root of 25 x squared minus 10 x plus 6 end root end cell end tableadalah -2.

Pembahasan

Diperhatikan limit bentuk tak tentu begin mathsize 14px style infinity minus infinity end style berikut.

begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root close parentheses equals L end style 

  • begin mathsize 14px style L equals negative infinity end style jika dan hanya jika begin mathsize 14px style a less than p end style
  • L equals fraction numerator b minus q over denominator 2 square root of a end fraction jika dan hanya jika begin mathsize 14px style a equals p end style
  • begin mathsize 14px style L equals infinity end style jika dan hanya jika begin mathsize 14px style a greater than p end style

sehingga

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack L i m with x rightwards arrow infinity below 5 x minus 3 minus square root of 25 x squared minus 10 x plus 6 end root end cell equals cell stack L i m with x rightwards arrow infinity below square root of open parentheses 5 x minus 3 close parentheses squared end root minus square root of 25 x squared minus 10 x plus 6 end root end cell row blank equals cell stack L i m with x rightwards arrow infinity below square root of 25 x squared minus 30 x plus 9 end root minus square root of 25 x squared minus 10 x plus 6 end root end cell row blank equals cell fraction numerator b minus q over denominator 2 square root of a end fraction space space space space space space space space end cell row blank equals cell fraction numerator negative 30 plus 10 over denominator 2 square root of 25 end fraction end cell row blank equals cell fraction numerator negative 20 over denominator 10 end fraction end cell row blank equals cell negative 2 end cell row blank blank blank row blank blank blank end table end style

Jadi, nilai table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell stack l i m with x rightwards arrow infinity below end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x 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 3 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 square root of 25 x squared minus 10 x plus 6 end root end cell end tableadalah -2.

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