Roboguru

Nilai dari:

Nilai dari:

begin mathsize 14px style limit as x rightwards arrow infinity of space square root of x squared plus x minus 2 end root minus square root of x squared minus 3 x plus 1 end root equals... end style 

Jawaban:

Gunakan konsep limit tak hingga bentuk akar.

begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses 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 close parentheses equals open curly brackets table attributes columnalign left end attributes row cell infinity comma space a greater than p end cell row cell fraction numerator b minus q over denominator 2 square root of a end fraction comma space a equals p end cell row cell negative infinity comma space a less than p end cell end table close end style 

Perhatikan perhitungan berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as x rightwards arrow infinity of open parentheses square root of x squared plus x minus 2 end root minus square root of x squared minus 3 x plus 1 end root close parentheses end cell equals cell fraction numerator 1 minus open parentheses negative 3 close parentheses over denominator 2 square root of 1 end fraction end cell row blank equals cell fraction numerator 1 plus 3 over denominator 2 cross times 1 end fraction end cell row blank equals cell 4 over 2 end cell row cell limit as x rightwards arrow infinity of open parentheses square root of x squared plus x minus 2 end root minus square root of x squared minus 3 x plus 1 end root close parentheses end cell equals 2 end table end style 

Jadi, diperoleh nilai limit tak hingga bentuk akar tersebut adalah 2.

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