Roboguru

begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of 2 x plus 2 end root minus square root of 2 x minus 1 end root close parentheses open parentheses square root of 2 x plus 5 end root close parentheses equals end style  

Jawaban:

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 r end root space a equals p rightwards double arrow fraction numerator b minus q over denominator 2 square root of a end fraction  limit as x rightwards arrow infinity of left parenthesis square root of 2 x plus 2 end root minus square root of 2 x minus 1 end root right parenthesis left parenthesis square root of 2 x plus 5 end root right parenthesis equals limit as x rightwards arrow infinity of left parenthesis square root of 2 x plus 2 end root right parenthesis left parenthesis square root of 2 x plus 5 end root right parenthesis minus left parenthesis square root of 2 x minus 1 end root right parenthesis left parenthesis square root of 2 x plus 5 end root right parenthesis equals limit as x rightwards arrow infinity of square root of open parentheses 2 x plus 2 close parentheses open parentheses 2 x plus 5 close parentheses end root minus square root of open parentheses 2 x minus 1 close parentheses open parentheses 2 x plus 5 close parentheses end root equals limit as x rightwards arrow infinity of square root of 4 x squared plus 14 x plus 10 end root minus square root of 4 x squared plus 8 x minus 5 end root equals fraction numerator b minus q over denominator 2 square root of a end fraction equals fraction numerator 14 minus 8 over denominator 2 square root of 4 end fraction equals 6 over 4 equals 3 over 2  end style 

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