$\lim\limits_{x\to\infty}({\sqrt{2x^2+5x+8}}-\sqrt{2x^2+2x-1})=\dots$
A. $\frac{3}{2\sqrt{2}}$
B. $\frac{3}{4}\sqrt{2}$
C. $-\frac{3}{2\sqrt{2}}$
D. $-\frac{3}{4\sqrt{2}}$
E. $3$
Penyelesaian
PERINGATAN!!
$\lim\limits_{x\to \infty}(\sqrt{ax^2+bx+c}-\sqrt{ax^2+qx+c})$ maka dapat diseleaikan dengan $\frac{b-q}{2\sqrt{a}}$
Jawaban
$\lim\limits_{x\to\infty}({\sqrt{2x^2+5x+8}}-\sqrt{2x^2+2x-1})=\dots$
$a=2$
$b=5$
$q=2$
$\frac{b-q}{2\sqrt{a}}$
$=\frac{5-2}{2\sqrt{2}}$
$=\frac{3}{2\sqrt{2}}$
$=\frac{3}{2\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$
$=\frac{3\sqrt{2}}{2\times 2}$
$=\frac{3\sqrt{2}}{4}$
$=\frac{3}{4}\sqrt{2}$
Kesimpulan
Jadi nilai $\lim\limits_{x\to\infty}({\sqrt{2x^2+5x+8}}-\sqrt{2x^2+2x-1})=\frac{3}{4}\sqrt{2}$
Jawaban: B
Muda Berkarya Intelektual Normatif