B

1003108806

Level: 
B
We are given the equation \[ \sum\limits_{n=1}^{\infty}(x+2)^{2n} =\frac13 \] with the unknown \( x \) being a real number. What is the set of all its solutions?
\( \left\{ -\frac32,-\frac52 \right\} \)
\( \left\{ -\frac32\right\} \)
\( \left\{ -\frac52 \right\} \)
\( \left\{\ \right\} \)
\( \left\{ \frac32,\frac52 \right\} \)

1003230206

Level: 
B
Which of the statements A, B, C, D given bellow are incorrect? \[ \begin{array}{l} \text{A: }\left(\ln\frac x2\right)'=\frac1x,\ x\in\mathbb{R}^+ \\ \text{B: }\left(5\sin⁡3x\right)'=5\cos⁡3x \\ \text{C: }\left(\frac1{\left(x^3-1\right)^2}\right)'=\frac{-6x^2}{\left(x^3-1\right)^3},\ x\in\mathbb{R}\setminus\{1\} \\ \text{D: }\left(\ln⁡(1+\cos⁡ x ) \right)'=\frac1{1-\sin ⁡x},\ x\neq\frac{\pi}2+2k\pi,\ k\in\mathbb{Z} \end{array}\] The only incorrect statements are:
B, D
A, B, D
B, C
B
A, C
A, C, D

1003230205

Level: 
B
Which of the statements A, B, C given bellow are correct? \[ \begin{array}{l} \text{A: } \left(\frac{2x-1}{2-x}\right)'=\frac{5-4x}{(2-x)^2},\ x\neq2 \\ \text{B: } \left(\frac{\mathrm{e}^x-1}{x}\right)'=\frac{\mathrm{e}^x(x-1)-1}{x^2},\ x\neq0 \\ \text{C: } \left(\frac{\cos⁡ x}{1-\sin ⁡x}\right)'=\frac1{1-\sin ⁡x},\ x\neq\frac{\pi}2+2k\pi,\ k\in\mathbb{Z} \end{array}\] The only correct statements are:
C
A, C
A, B
B
A
B, C