After rationalizing the denominator, (1)/(√(3) - 1) equals:

(1)/(√(3) - 1) · (√(3) + 1)/(√(3) + 1) = (√(3) + 1)/(3 - 1) = (√(3) + 1)/(2).

The solution set of x^2 > 9 in ℝ is:

x^2 > 9 ⇔ |x| > 3 ⇔ x 3. Solution: (-∞, -3) ∪ (3, +∞).

Problems & worked solutions

RO M1

After rationalizing the denominator, $\frac{1}{\sqrt{3} - 1}$ equals:

Show answer & worked solution

$\frac{1}{\sqrt{3} - 1} \cdot \frac{\sqrt{3} + 1}{\sqrt{3} + 1} = \frac{\sqrt{3} + 1}{3 - 1} = \frac{\sqrt{3} + 1}{2}$ .

RO M1

The solution set of $x^{2} > 9$ in $R$ is:

Show answer & worked solution

$x^{2} > 9 \Leftrightarrow ∣ x ∣ > 3 \Leftrightarrow x < - 3$ or $x > 3$ . Solution: $(- \infty, - 3) \cup (3, + \infty)$ .

RO M1

$\int x \cos x d x$ equals:

Show answer & worked solution

$u = x$ , $d u = d x$ , $v = \sin x$ . $\int x \cos x d x = x \sin x - \int \sin x d x = x \sin x + \cos x + C$ .

Problems & worked solutions

RO M1

After rationalizing the denominator, $\frac{1}{\sqrt{3} - 1}$ equals:

Show answer & worked solution

$\frac{1}{\sqrt{3} - 1} \cdot \frac{\sqrt{3} + 1}{\sqrt{3} + 1} = \frac{\sqrt{3} + 1}{3 - 1} = \frac{\sqrt{3} + 1}{2}$ .

RO M1

The solution set of $x^{2} > 9$ in $R$ is:

Show answer & worked solution

$x^{2} > 9 \Leftrightarrow ∣ x ∣ > 3 \Leftrightarrow x < - 3$ or $x > 3$ . Solution: $(- \infty, - 3) \cup (3, + \infty)$ .

RO M1

$\int x \cos x d x$ equals:

Show answer & worked solution

$u = x$ , $d u = d x$ , $v = \sin x$ . $\int x \cos x d x = x \sin x - \int \sin x d x = x \sin x + \cos x + C$ .