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begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 8 x plus 7 end root minus square root of 4 x squared plus 2 x minus 1 end root close parentheses end style 

N. Puspita

Master Teacher

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Jawaban

nilai dari begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 8 x plus 7 end root minus square root of 4 x squared plus 2 x minus 1 end root close parentheses end style adalah begin mathsize 14px style negative 5 over 2 end style

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 limit as x rightwards arrow infinity of space left parenthesis square root of 4 x squared minus 8 x plus 7 end root minus square root of 4 x squared plus 2 x minus 1 end root right parenthesis space equals fraction numerator b minus q over denominator 2 square root of a end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator negative 8 minus 2 over denominator 2 square root of 4 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator negative 10 over denominator 4 end fraction equals fraction numerator negative 5 over denominator 2 end fraction end style   

Jadi, nilai dari begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 8 x plus 7 end root minus square root of 4 x squared plus 2 x minus 1 end root close parentheses end style adalah begin mathsize 14px style negative 5 over 2 end style

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