B | math4u.vsb.cz

9000063109

Level:

Differentiate the following function. \[ f(x) = 3^{x}\cdot x^{3} \]

\(f'(x) = 3^{x}x^{2}(x\ln 3 + 3),\ x\in \mathbb{R}\)

\(f'(x) = 3^{x+1}x^{2}\ln 3,\ x\in \mathbb{R}\)

\(f'(x) = 3^{x}x^{2}(x + 3),\ x\in \mathbb{R}\)

\(f'(x) = 3^{x}x^{2}(x\ln x + 3),\ x\in \mathbb{R}^{+}\)

9000046607

Level:

Identify an inequality which is true for both \(x = \frac{4\pi } {3}\) and \(x = \frac{5\pi } {3}\).

\(\sin x < \frac{1} {2}\)

\(\mathop{\mathrm{tg}}\nolimits x > 0\)

\(\cos x < 0\)

\(\mathop{\mathrm{cotg}}\nolimits x\leq - 1\)

9000062410

Level:

Find the line perpendicular to the graph of the function \(f(x) = x^{3}\) at the point \(T = [-1,y_{0}]\).

\(x + 3y + 4 = 0\)

\(3x - y + 2 = 0\)

\(3x + y - 4 = 0\)

\(x - 3y - 2 = 0\)

9000060603

Level:

Identify the real number \(x\) which ensures that the numbers \(a_{1} = -x\), \(a_{2} = -5\) and \(a_{3} = 0\) are three consecutive terms of an arithmetic sequence.

\(x = 10\)

\(x = 0\)

\(x = -5\)

\(x = 5\)

\(x = -10\)

9000046608

Level:

Identify an inequality which is true for both \(x = \frac{\pi } {6}\) and \(x = -\frac{\pi }{6}\).

\(\cos x > 0\)

\(\sin x > \frac{1} {2}\)

\(|\mathop{\mathrm{tg}}\nolimits x| < \frac{1} {2}\)

\(\mathop{\mathrm{cotg}}\nolimits x\leq - 1\)

9000060606

Level:

Identify the real number \(x\) which ensures that the numbers \(a_{1} = 5x + 1\), \(a_{2} = x\) and \(a_{3} = 7x + 3\) are three consecutive terms of an arithmetic sequence.

\(x = -0.4\)

\(x = 0.4\)

\(x = 2.5\)

\(x = -2.5\)

\(x = 5\)

9000060602

Level:

Identify the real number \(x\) which ensures that the numbers \(a_{1} = -12\), \(a_{2} = x\) and \(a_{3} = 24\) are three consecutive terms of an arithmetic sequence.

\(x = 6\)

\(x = 0\)

\(x = 12\)

\(x = -24\)

\(x = -2\)

9000060610

Level:

Identify the real number \(x\) which ensures that the numbers \(a_{1} =\log x\), \(a_{2} = 2\) and \(a_{3} =\log x^{3}\) are three consecutive terms of an arithmetic sequence.

\(x = 10\)

\(x = 0\)

\(x = 0.1\)

\(x = 1\)

\(x = -1\)

9000060604

Level:

Identify the real number \(x\) which ensures that the numbers \(a_{1} = x\), \(a_{2} = x + 2\) and \(a_{3} = 2x\) are three consecutive terms of an arithmetic sequence.

\(x = 4\)

\(x = 0\)

\(x = 2\)

\(x = 6\)

\(x = 8\)

A semicircle is a half of the full circle. An infinite spiral is built from semicircles with an increasing radius. The radius of the first semicircle is \(2\, \mathrm{cm}\). The radius of each semicircle in the spiral is a double of the radius of the previous semicircle. Find the total length of the spiral.

\(\infty \)

\(4\pi \)

\(\frac{4} {3}\pi \)

\(- 4\pi \)

B

9000063109

9000046607

9000062410

9000060603

9000046608

9000060606

9000060602

9000060610

9000060604

9000062905

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