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Nilai dari x→∞lim​(4x2−4x+1​−4x2−3x+6​)=…

Pertanyaan

Nilai dari limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 4 x plus 1 end root minus square root of 4 x squared minus 3 x plus 6 end root close parentheses equals horizontal ellipsis  

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

hasil dari limit tersebut adalah negative 1 fourth.

Pembahasan

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 L 

Dimana:

(1) Jika a equals p maka L equals fraction numerator b minus q over denominator 2 square root of a end fraction 

(2) JIka a greater than p maka L equals infinity 

(3) Jika a less than p maka L equals negative infinity 

limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 4 x plus 1 end root minus square root of 4 x squared minus 3 x plus 6 end root close parentheses 

Karena pada soal diatas memenuhi sifat limit tersebut dimana a = p, maka akan digunakan rumus pertama.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 4 x plus 1 end root minus square root of 4 x squared minus 3 x plus 6 end root close parentheses end cell equals cell fraction numerator negative 4 minus open parentheses negative 3 close parentheses over denominator 2 square root of 4 end fraction end cell row blank equals cell fraction numerator negative 4 plus 3 over denominator 2 cross times 2 end fraction end cell row blank equals cell negative 1 fourth end cell end table 

Dengan demikian, hasil dari limit tersebut adalah negative 1 fourth.

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