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9000064008

Level:

Find the limit of the following sequence.

{(\frac{(n^{2} + 2 n + 1)^{n}}{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

e^{2}

2 e

e + 2

\infty

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

9000062406

Level:

Identify an asymptote to the graph of the following function.

f (x) = \frac{x^{2} + 4}{x}

y = x

y = x + 1

y = x - 1

y = - x

9000039103

Level:

Assuming

x \in R

y \in R

, solve the following equation.

(2 + 5 i) x + (1 - i) y = 13 i + 8

x = 3, y = 2

x = 13, y = 8

x = 8, y = 13

x = 2, y = 3

9000039104

Level:

Assuming

x \in R

y \in R

, solve the following equation.

(3 - 2 i) x + (5 - 7 i) y = 1 + 3 i

x = 2, y = - 1

x = - 1, y = 2

x = - 2, y = - 1

x = - 1, y = - 2

9000039109

Level:

Assuming

z \in C

, solve the following equation.

2 z - \overset{―}{i z} = 1 - i

z = 1 - i

z = 1 + i

z = \frac{1}{3} - \frac{1}{3} i

z = - \frac{1}{3} + \frac{1}{3} i

9000039110

Level:

Assuming

z \in C

, solve the following equation.

(1 + i \sqrt{3}) z = 1 - i \sqrt{3}

z = - \frac{1}{2} - \frac{\sqrt{3}}{2} i

z = \frac{\sqrt{3}}{2} + \frac{1}{2} i

z = - \frac{1}{2} + \frac{\sqrt{3}}{2} i

z = - \frac{\sqrt{3}}{2} + \frac{1}{2} i

9000039108

Level:

Assuming

z \in C

, solve the following equation. By

\overset{―}{z}

the complex conjugate of

z

is denoted.

2 z - i \overset{―}{z} = 1 - i

z = \frac{1}{3} - \frac{1}{3} i

z = 1 + i

z = - \frac{3}{5} + \frac{6}{5} i

z = - \frac{1}{5} - \frac{3}{5} i

C

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