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Pertanyaan

Tentukan nilai limit berikut.

limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 8 x plus 7 end root minus open parentheses 2 x minus 3 close parentheses close parentheses   

N. Puspita

Master Teacher

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Jawaban

 limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 8 x plus 7 end root minus open parentheses 2 x minus 3 close parentheses close parentheses equals 1.

Pembahasan

limit as x rightwards arrow negative infinity of 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 equals straight L  

Jika a equals p, maka straight L equals fraction numerator b minus q over denominator 2 square root of a end fraction 

Maka, hasil limit tersebut:

limit as x rightwards arrow infinity thin space of open parentheses square root of 4 x squared minus 8 x plus 7 end root minus open parentheses 2 x minus 3 close parentheses close parentheses equals limit as x rightwards arrow infinity thin space of open parentheses square root of 4 x squared minus 8 x plus 7 end root minus square root of open parentheses 2 x minus 3 close parentheses squared end root close parentheses equals limit as x rightwards arrow infinity thin space of open parentheses square root of 4 x squared minus 8 x plus 7 end root minus square root of 4 x squared minus 12 x plus 9 end root close parentheses equals fraction numerator b minus q over denominator 2 square root of a end fraction equals fraction numerator negative 8 minus left parenthesis negative 12 right parenthesis over denominator 2 square root of 4 end fraction equals fraction numerator 4 over denominator 2 times 2 end fraction equals 4 over 4 equals 1 

Jadi, limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 8 x plus 7 end root minus open parentheses 2 x minus 3 close parentheses close parentheses equals 1.

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