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Nilai dari

Nilai dari begin mathsize 14px style limit as x rightwards arrow infinity of 5 x minus 3 minus square root of 25 x squared minus 10 x plus 6 end root equals... end style

Jawaban:

Dengan menggunakan rumus berikut :

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 equals fraction numerator b minus q over denominator 2 square root of a end fraction end style

dengan a sama dengan p. Maka,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of 5 x minus 3 minus square root of 25 x squared minus 10 x plus 6 end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of open parentheses 5 x minus 3 close parentheses squared end root minus square root of 25 x squared minus 10 x plus 6 end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of 25 x squared minus 30 x plus 9 end root minus square root of 25 x squared minus 10 x plus 6 end root end cell row blank equals cell fraction numerator negative 30 minus left parenthesis negative 10 right parenthesis over denominator 2 square root of 25 end fraction end cell row blank equals cell fraction numerator negative 20 over denominator 10 end fraction end cell row blank equals cell negative 2 end cell end table end style 

Jadi, nilai limitnya adalah -2.

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