Nilai dari: x→∞lim​x2+x+2​−2x2+x−1​=....

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Nilai dari: begin mathsize 14px style limit as straight x rightwards arrow infinity of square root of straight x squared plus straight x plus 2 end root minus square root of 2 straight x squared plus straight x minus 1 end root equals.... end style 

N. Puspita

Master Teacher

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ii, Nilai  undefined 

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Pembahasan

Dengan menerapkan konsep limit tak hingga:

Jika: 

begin mathsize 14px style 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 equals straight L end style 

Maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight L equals cell infinity space left right double arrow straight a greater than straight p end cell row straight L equals cell negative infinity left right double arrow straight a less than straight p end cell row straight L equals cell fraction numerator straight b minus straight q over denominator 2 square root of straight a end fraction left right double arrow straight a equals straight p end cell end table end style 

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

Nilai: begin mathsize 14px style straight a equals 1 comma space straight p equals 2 end style sehingga diperoleh begin mathsize 14px style straight a less than straight p end style

Maka: begin mathsize 14px style limit as straight x rightwards arrow infinity of square root of straight x squared plus straight x plus 2 end root minus square root of 2 straight x squared plus straight x minus 1 end root equals negative infinity end style 

Jadiii, Nilai  undefined 

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