$\lim\limits_{x\to\infty}({\sqrt{2x^2+5x+8}}-\sqrt{2x^2+2x-1})=\dots$

lim_{x \to \infty} (\sqrt{2 x^{2} + 5 x + 8} - \sqrt{2 x^{2} + 2 x - 1}) = \dots

$lim_{x \to \infty} (\sqrt{2 x^{2} + 5 x + 8} - \sqrt{2 x^{2} + 2 x - 1}) = \dots$

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!!

$lim_{x \to \infty} (\sqrt{a x^{2} + b x + c} - \sqrt{a x^{2} + q x + c})$ maka dapat diseleaikan dengan $\frac{b - q}{2 \sqrt{a}}$

Jawaban

$lim_{x \to \infty} (\sqrt{2 x^{2} + 5 x + 8} - \sqrt{2 x^{2} + 2 x - 1}) = \dots$

$a = 2$

$b = 5$

$q = 2$

$\frac{b - q}{2 \sqrt{a}}$

$= \frac{5 - 2}{2 \sqrt{2}}$

$= \frac{3}{2 \sqrt{2}}$

$= \frac{3}{2 \sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$

$= \frac{3 \sqrt{2}}{2 \times 2}$

$= \frac{3 \sqrt{2}}{4}$

$= \frac{3}{4} \sqrt{2}$

Kesimpulan

Jadi nilai $lim_{x \to \infty} (\sqrt{2 x^{2} + 5 x + 8} - \sqrt{2 x^{2} + 2 x - 1}) = \frac{3}{4} \sqrt{2}$

Jawaban: B

        
          Muda Berkarya Intelektual Normatif

            Muda Berkarya Intelektual Normatif

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