B

1003068201

Level: 
B
The value of the integral \[ \frac{4\pi}9\int\limits_0^3 x^2\mathrm{d}x \] is a number which represents:
the volume of a cone with the base radius of \( 2\,\mathrm{cm} \) and the height of \( 3\,\mathrm{cm} \).
the volume of a cone with the base radius of \( 3\,\mathrm{cm} \) and the height of \( 2\,\mathrm{cm} \).
the volume of a sphere segment which is a part of a sphere with the radius of \( \frac23\,\mathrm{cm} \) and the height of \( 3\,\mathrm{cm} \).
volume of a sphere segment which is a part of a sphere with the radius of \( 3\,\mathrm{cm} \) and the height of \( \frac23\,\mathrm{cm} \).

1003261904

Level: 
B
Given the function \[ f(x)=\sin ⁡x-3\cos⁡ x\text{ ,} \] determine the set of all \( x \), \( x\in\mathbb{R} \), such that \( f''(x)+f(x)=0 \).
\( \mathbb{R} \)
\( \emptyset \)
\( \{k\pi;\ k\in\mathbb{Z}\} \)
\( \left\{(2k+1)\frac{\pi}2;\ k\in\mathbb{Z} \right\} \)