B | math4u.vsb.cz

9000065907

Level:

Evaluate the following integral on \(\mathbb{R}\). \[ \int \frac{x^{4} - 1} {x^{2} + 1}\, \text{d}x \]

\(\frac{1} {3}x^{3} - x + c,\ c\in \mathbb{R}\)

\(\frac{1} {3}x^{3} + x + c,\ c\in \mathbb{R}\)

\(\frac{1} {5}x^{5} - x +\ln |x^{2} - 1| + c,\ c\in \mathbb{R}\)

\(3x^{2} -\ln |x^{2} - 1| + c,\ c\in \mathbb{R}\)

9000068705

Level:

Identify the real number \(x\) which converts the numbers \(a_{1} = x - 6\), \(a_{2} = x\) and \(a_{3} = -x\) into three consecutive numbers of a geometric series.

\(x = 3\)

\(x = 0\)

\(x = 2\)

\(x = 2.5\)

\(x = -12\)

9000066003

Level:

Evaluate the following integral on \(\mathbb{R}\). \[ \int x\cos x\, \mathrm{d}x \]

\(x\sin x +\cos x + c,\ c\in \mathbb{R}\)

\(- x\cos x +\sin x + c,\ c\in \mathbb{R}\)

\(x\cos x -\sin x + c,\ c\in \mathbb{R}\)

\(x\sin x -\cos x + c,\ c\in \mathbb{R}\)

9000068706

Level:

Identify the real number \(x\) which converts the numbers \(a_{1} = x + 14\), \(a_{2} = x + 2\) and \(a_{3} = x - 4\) into three consecutive numbers of a geometric series.

\(x = 10\)

\(x = 5\)

\(x = 2.5\)

\(x = 2\)

\(x = -5\)

9000068704

Level:

Identify the real number \(x\) which converts the numbers \(a_{1} = x\), \(a_{2} = x + 5\) and \(a_{3} = 4x\) into three consecutive numbers of a geometric series.

\(x = 5\)

\(x = 1\)

\(x = 2\)

\(x = 3\)

\(x = 4\)

9000069910

Level:

Find the values of the parameter \(p\in \mathbb{R}\) which guarantee that the equation \[ x^{2} + 2px + 16 = 0 \] has solution with a nonzero imaginary part.

\(p\in (-4,4)\)

\(p\in (-\infty ,4)\)

\(p\in (4,\infty )\)

\(p\in \emptyset\)

9000068707

Level:

Identify the real number \(x\) which converts the numbers \(a_{1} = x^{2} - 110\), \(a_{2} = x^{2}\) and \(a_{3} = x^{2} - 1\: 100\) into three consecutive numbers of a geometric series.

\(x = -10\)

\(x = -1\)

\(x = -2\)

\(x = -4\)

\(x = -110\)

9000065901

Level:

Evaluate the following integral on the interval \((-1,+\infty)\). \[ \int \frac{1} {x + 1}\, \text{d}x \]

\(\ln |x + 1| + c,\ c\in \mathbb{R}\)

\(\ln |x| + c,\ c\in \mathbb{R}\)

\(\frac{1} {x} + c,\ c\in \mathbb{R}\)

\(-\frac{1} {2}(x + 1)^{-2} + c,\ c\in \mathbb{R}\)

9000068709

Level:

Identify the real number \(x\) which converts the numbers \(a_{1} =\log x\), \(a_{2} = 2 +\log x\) and \(a_{3} = 4\log x\) into three consecutive numbers of a geometric series.

\(x = 100\)

\(x = 1\)

\(x =\log 2\)

\(x = 2\)

\(x = 10\)

9000065903

Level:

Evaluate the following integral on the interval \((-6,+\infty)\). \[ \int \frac{1} {6x + 36}\, \text{d}x \]

\(\frac{1} {6}\ln |x + 6| + c,\ c\in \mathbb{R}\)

\(-\frac{1} {2}(6x + 36)^{-2} + c,\ c\in \mathbb{R}\)

\(6\ln |x + 6| + c,\ c\in \mathbb{R}\)

\(12x^{2} + 36x + c,\ c\in \mathbb{R}\)

B

9000065907

9000068705

9000066003

9000068706

9000068704

9000069910

9000068707

9000065901

9000068709

9000065903

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