$\lim\limits_{x\to\infty}(\sqrt{x^2+2x+1}-\sqrt{x^2-3x+4})=\dots$

lim_{x \to \infty} (\sqrt{x^{2} + 2 x + 1} - \sqrt{x^{2} - 3 x + 4}) = \dots

$lim_{x \to \infty} (\sqrt{x^{2} + 2 x + 1} - \sqrt{x^{2} - 3 x + 4}) = \dots$

A. $- \frac{5}{2}$

B. $- 2$

C. $\frac{2}{5}$

D. $\frac{3}{2}$

E. $\frac{5}{2}$

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

$lim_{x \to \infty} (\sqrt{x^{2} + 2 x + 1} - \sqrt{x^{2} - 3 x + 4}) = \dots$

$a = 1$

$b = 2$

$q = - 3$

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

$= \frac{2 - (- 3)}{2 \sqrt{1}}$

$= \frac{5}{2}$

Kesimpulan

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

Jawaban: E

        
          Muda Berkarya Intelektual Normatif

            Muda Berkarya Intelektual Normatif

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