Nilai dari x→∞lim​ (x+1)−x2+8x−5​ adalah ...

Pertanyaan

Nilai dari limit as x rightwards arrow infinity of space open parentheses x plus 1 close parentheses minus square root of x squared plus 8 x minus 5 end root adalah ...

  1. 0

  2. tilde

  3. negative 3

  4. 2

  5. 3

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

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

 

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space open parentheses x plus 1 close parentheses minus square root of x squared plus 8 x minus 5 end root end cell equals cell limit as x rightwards arrow infinity of space square root of open parentheses x plus 1 close parentheses squared end root minus square root of x squared plus 8 x minus 5 end root end cell row blank equals cell limit as x rightwards arrow infinity of space square root of x squared plus 2 x plus 1 end root minus square root of x squared plus 8 x minus 5 end root end cell end table

 

karena a equals p equals 1 sehingga nilai limitnya didapat dengan menggunakan rumus fraction numerator b minus q over denominator 2 square root of a end fraction. maka :

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space square root of x squared plus 2 x plus 1 end root minus square root of x squared plus 8 x minus 5 end root end cell equals cell fraction numerator b minus q over denominator 2 square root of a end fraction end cell row blank equals cell fraction numerator 2 minus 8 over denominator 2 square root of 1 end fraction end cell row blank equals cell fraction numerator negative 6 over denominator 2 end fraction end cell row blank equals cell negative 3 end cell end table

 

 

Nilai dari limit as x rightwards arrow infinity of space open parentheses x plus 1 close parentheses minus square root of x squared plus 8 x minus 5 end root adalah negative 3.

Jadi, jawaban yang tepat adalah C.

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