C | math4u.vsb.cz

9000064807

Level:

Find the sum of the integers which satisfy the following inequality.

x^{2} - 8 x - 153 \leq 0

108

162

91

78

56

9000064009

Level:

Find the limit of the following sequence.

{({(\frac{\sqrt[n]{2}}{n} + \sqrt[n]{2})}^{n})}_{n = 1}^{\infty}

Hint: The limit of the sequence

{({(1 + \frac{1}{n})}^{n})}_{n = 1}^{\infty}

is the Euler number

e

2 e

e^{2}

e + 2

\infty

9000064010

Level:

Find the limit of the following sequence.

{({(\frac{2 n + 1}{n})}^{n})}_{n = 1}^{\infty}

Hint: The limit of the sequence

{({(1 + \frac{1}{n})}^{n})}_{n = 1}^{\infty}

is the Euler number

e

\infty

2 e

e^{2}

e + 2

9000063610

Level:

Find the following limit.

lim_{n \to \infty} \frac{3 + 6 + 9 + \dots + 3 n}{6 + 12 + 18 + \dots + 6 n}

\frac{1}{2}

0

1

\infty

9000063303

Level:

Differentiate the following function.

f (x) = \sqrt{\sin x}

f^{'} (x) = \frac{\cos x}{2 \sqrt{\sin x}}, x \in ⋃_{k \in Z} (2 k π; π + 2 k π)

f^{'} (x) = \frac{\sin x}{2 \sqrt{\cos x}}, x \in ⋃_{k \in Z} (2 k π; \frac{π}{2} + 2 k π)

f^{'} (x) = \frac{1}{2 \sqrt{\sin x}}, x \in ⋃_{k \in Z} (2 k π; π + 2 k π)

f^{'} (x) = \frac{\cos x}{2 \sqrt{\sin x}}, x \in ⋃_{k \in Z} [2 k π; \frac{π}{2} + 2 k π]

9000063304

Level:

Differentiate the following function.

f (x) = \ln \sqrt{x}

f^{'} (x) = \frac{1}{2 x}, x > 0

f^{'} (x) = \frac{1}{2 x}, x \neq 0

f^{'} (x) = \frac{1}{x}, x > 0

f^{'} (x) = \frac{1}{x}, x \neq 0

9000063305

Level:

Differentiate the following function.

f (x) = \sqrt{\frac{x - 1}{x + 1}}

f^{'} (x) = \frac{1}{(x + 1)^{2}} \sqrt{\frac{x + 1}{x - 1}}, x \in (- \infty; - 1) \cup (1; \infty)

f^{'} (x) = \frac{\sqrt{x - 1}}{(x - 1)^{2} \sqrt{x + 1}}, x \in (- \infty; - 1) \cup [1; \infty)

f^{'} (x) = \frac{x - 1}{2 \sqrt{(x + 1)^{3}}}, x \neq - 1

f^{'} (x) = \frac{x - 1}{\sqrt{(x + 1)^{3}}}, x \in (- \infty; - 1) \cup [1; \infty)

9000063306

Level:

Differentiate the following function.

f (x) = e^{\sin 2 x}

f^{'} (x) = 2 e^{\sin 2 x} \cos 2 x, x \in R

f^{'} (x) = x e^{\sin 2 x} \cos 2 x, x \in R

f^{'} (x) = e^{\sin 2 x} \sin 2 x, x \in R

f^{'} (x) = e^{\cos 2 x}, x \in R

9000063307

Level:

Differentiate the following function.

f (x) = \ln (\cos 2 x)

f^{'} (x) = - 2 tg 2 x, x \in ⋃_{k \in Z} (- \frac{π}{4} + k π; \frac{π}{4} + k π)

f^{'} (x) = 2 tg 2 x, x \in ⋃_{k \in Z} (- \frac{π}{4} + k π; \frac{π}{4} + k π)

f^{'} (x) = - 2, x \in ⋃_{k \in Z} (- \frac{π}{4} + k π; \frac{π}{4} + k π)

f^{'} (x) = 1 - \ln (\sin 2 x), x \in ⋃_{k \in Z} (k π; \frac{π}{2} + k π)

9000063308

Level:

Differentiate the following function.

f (x) = \frac{1}{\ln x}

f^{'} (x) = \frac{- 1}{x \ln^{2} x}, x > 0, x \neq 1

f^{'} (x) = \ln x, x > 0

f^{'} (x) = \frac{\ln x}{x}, x \neq 0

f^{'} (x) = \frac{1}{x \ln^{2} x}, x \neq 0

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