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x→∞lim​x(4x+5)​−4x2−3​

Pertanyaan

begin mathsize 14px style limit as x rightwards arrow infinity of square root of x open parentheses 4 x plus 5 close parentheses end root minus square root of 4 x squared minus 3 end root end style 

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style limit as x rightwards arrow infinity of square root of x left parenthesis 4 x plus 5 right parenthesis end root minus square root of 4 x squared minus 3 end root equals 5 over 4 end style 

Pembahasan

Untuk menyelesaian limit tak hingga bentuk akar berlaku:

begin mathsize 14px style limit as x rightwards arrow 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 c end root equals straight L straight L equals negative infinity space left right double arrow space a less than p straight L equals fraction numerator b minus q over denominator 2 square root of a end fraction space left right double arrow space a equals p straight L equals infinity space left right double arrow space a greater than p end style 
 

    begin mathsize 14px style limit as x rightwards arrow infinity of square root of x left parenthesis 4 x plus 5 right parenthesis end root minus square root of 4 x squared minus 3 end root equals limit as x rightwards arrow infinity of square root of 4 x squared plus 5 x end root minus square root of 4 x squared minus 3 end root equals fraction numerator b minus q over denominator 2 square root of a end fraction space space equals fraction numerator 5 minus 0 over denominator 2 square root of 4 end fraction equals fraction numerator 5 over denominator 2 times 2 end fraction equals 5 over 4 end style  

Jadi, begin mathsize 14px style limit as x rightwards arrow infinity of square root of x left parenthesis 4 x plus 5 right parenthesis end root minus square root of 4 x squared minus 3 end root equals 5 over 4 end style 

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