B

9000065506

Časť: 
B
Vypočítajte \(\int \frac{x^{2}} {\sqrt{x}}\, \mathrm{d}x\) na intervale \((0;+\infty)\).
\(\frac{2} {5}x^{2}\sqrt{x} + c,\ c\in\mathbb{R}\)
\(\frac{2\sqrt{x}} {x} + c,\ c\in\mathbb{R}\)
\(\frac{2} {5}x\sqrt{x} + c,\ c\in\mathbb{R}\)
\(\frac{\sqrt{x}} {x} + c,\ c\in\mathbb{R}\)

9000065505

Časť: 
B
Určte \(\int (x^{2} + 3)(x^{2} - 1)\, \mathrm{d}x\) na \(\mathbb{R}\).
\(\frac{1} {5}x^{5} + \frac{2} {3}x^{3} - 3x + c,\ c\in\mathbb{R}\)
\((\frac{1} {3}x^{3} + 3x)(\frac{1} {3}x^{3} - x) + c,\ c\in\mathbb{R}\)
\(4x^{2} + c,\ c\in\mathbb{R}\)
\(4x^{3} + 4x + c,\ c\in\mathbb{R}\)

9000064503

Časť: 
B
Nájdite hodnoty reálnych koeficientov \(a\), \(b\) a \(c\) tak, aby kvadratická rovnica \[ ax^{2} + bx + c = 0 \] mala komplexné korene \(x_{1, 2} =\pm \mathrm{i}\frac{\sqrt{5}} {3} \).
\(a = 9\text{, }b = 0\text{, }c = 5\)
\(a = 5\text{, }b = 0\text{, }c = 9\)
\(a = 9\text{, }b = 0\text{, }c = -5\)
\(a = 5\text{, }b = 0\text{, }c = -9\)

9000064504

Časť: 
B
Nájdite hodnoty reálnych koeficientov \(a\), \(b\) a \(c\) tak, aby kvadratická rovnica \[ ax^{2} + bx + c = 0 \] mala komplexné korene \(x_{1, 2} = 1\pm \frac{\mathrm{i}} {2}\).
\(a = 4\text{, }b = -8\text{, }c = 5\)
\(a = 1\text{, }b = -4\text{, }c = 5\)
\(a = 4\text{, }b = 8\text{, }c = 5\)
\(a = 1\text{, }b = 4\text{, }c = 5\)