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

Pertanyaan

Nilai dari $\lim_{x\rightarrow\infty}\left(\sqrt{4x^2-4x+1}-\sqrt{4x^2-3x+6}\right)=\dots$

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 .