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x→∞lim​(5x+1)−25x2−10x+4​=

Pertanyaan

begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses 5 x plus 1 close parentheses minus square root of 25 x squared minus 10 x plus 4 end root equals end style  

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow infinity of square root of ax squared plus bx plus straight c end root minus square root of px squared plus qx plus straight r end root end cell row straight a equals cell straight p rightwards double arrow fraction numerator straight b minus straight q over denominator 2 square root of straight a end fraction end cell row blank blank blank row blank blank cell limit as straight x rightwards arrow infinity of left parenthesis 5 straight x plus 1 right parenthesis minus square root of 25 straight x squared minus 10 straight x plus 4 end root end cell row blank equals cell limit as straight x rightwards arrow infinity of square root of left parenthesis 5 straight x plus 1 right parenthesis squared end root minus square root of 25 straight x squared minus 10 straight x plus 4 end root end cell row blank equals cell limit as straight x rightwards arrow infinity of square root of 25 straight x squared plus 10 straight x plus 1 end root minus square root of 25 straight x squared minus 10 straight x plus 4 end root end cell row blank equals cell fraction numerator straight b minus straight q over denominator 2 square root of straight a end fraction end cell row blank equals cell fraction numerator 10 minus left parenthesis negative 10 right parenthesis over denominator 2 square root of 25 end fraction end cell row blank equals cell fraction numerator 10 plus 10 over denominator 2 times 5 end fraction end cell row blank equals cell 20 over 10 end cell row blank equals 2 end table end style 

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