B

9000065504

Část: 
B
Vypočtěte \(\int (1 -\sqrt{x})(1 + \sqrt{x})\, \mathrm{d}x\) na intervalu \((0;+\infty)\).
\(x -\frac{1} {2}x^{2} + c,\ c\in\mathbb{R}\)
\((x -\frac{1} {2}x^{2})(x + \frac{1} {2}x^{2}) + c,\ c\in\mathbb{R}\)
\(x -\frac{1} {2}x^{\frac{1} {2} } + c,\ c\in\mathbb{R}\)
\((x -\frac{1} {2}x^{-\frac{1} {2} })(x + \frac{1} {2}x^{-\frac{1} {2} }) + c,\ c\in\mathbb{R}\)

9000065506

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

9000065505

Část: 
B
Určete \(\int (x^{2} + 3)(x^{2} - 1)\, \mathrm{d}x\) 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

Část: 
B
Kvadratická rovnice \(ax^{2} + bx + c = 0\) s komplexními kořeny \(x_{1, 2} =\pm \mathrm{i}\frac{\sqrt{5}} {3} \) má koeficienty:
\(a = 9\text{, }b = 0\text{, }c = 5\)
\(a = 5\text{, }b = 0\text{, }c = 9\)
\(a = 9\text{, }b = 0\text{, }c = -5\)
\(a = 5\text{, }b = 0\text{, }c = -9\)