1

Find the equation of the tangent line to the curve \$ g(x) = 4sin(2x) \$ at \$ x = (5π)/6 \$.

A) \$ y = 4x − (10π)/3 ​+ 2\sqrt(3) \$​

B) \$ y = 2x − (10π)/3 ​+ 2\sqrt(3) \$​

C) \$ y = 4x − (7π)/3 ​+ 2\sqrt(3) \$​

D) \$ y = 2x − (10π)​ + 2\sqrt(6) \$​

2

Evaluate \$\int(5/(cos u cot u))du\$.

A) sinu + C

B) secu + C

C) 5sinu + C

D) 5secu + C

3

Find the sum of the series: 2 + 6 + 18 + 54 + 162 + … + 4374.

A) 5550

B) 6560

C) 6500

D) 6750

4

Convert each number to a rectangular form \$ 20 cos ((7pi)/4) \$.

A) \$ -10 sqrt(4) - 10 sqrt(2)i \$

B) \$ -11 sqrt(2) - 5 sqrt(2)i \$

C) \$ 10 sqrt(2) - 10 sqrt(2)i \$

D) \$ 11 sqrt(2) + 10 sqrt(2)i \$

5

Determine whether the following sequences converge or diverge. If they converge, find the limit. \$ a_n = (1/n) \$.

A) Diverges

B) Invalid

C) Not diverges

D) converges, and its limit is 0.

6

Find the derivative of \$f(x) = (4x^2 + 3x - 2)^5\$.

A) \$5(4x^2 + 4x - 2)^4 (8x + 5)\$

B) \$(4x^2 - 3x - 2)^4 (8x + 5)^5\$

C) \$5(4x^2 + 3x - 2)^4 (8x + 3)\$

D) \$(4x^2 + 3x - 2)^4 (8x + 3)\$

7

Evaluate the integral \$\int(3x^2 + 4x − 5)dx\$.

A) \$x^3 + 2x^2 − 5x + C\$

B) \$x^3 + 2x^2 − 5x\$

C) \$x^3 + 2x^2 − 5x - C\$

D) \$x^3 + 2x^2 − 5x + 7 + C\$

8

Evaluate the sum of the infinite series: \$S = 1 + 1/8 + 1/(27) + 1/(64) + 1/(125) + ...+1/(n^4)\$.

A) \$ (pi^4)/(80)\$

B) \$ (pi^4)/(90)\$

C) \$ (pi^8)/(90)\$

D) \$ (pi^8)/(80)\$

9

Convert each number to polar form \$ - 8sqrt(2) - 8i sqrt(2) \$.

A) \$ 8 (cos ((pi)/4))+i (sin ((pi)/4)) \$

B) \$ -16 (cos ((pi)/4)) - i (sin ((pi)/4)) \$

C) \$ 16 (cos ((5pi)/4)) + i (sin ((5pi)/4)) \$

D) \$ 16 (cos ((pi)/4)) - i (sin ((pi)/4)) \$

10

Solve the equation \$ z^2 + 3z +13 = 0\$ for complex z.

A) \$-3/2 pm (i sqrt(43​))/2\$

B) \$ (3 + sqrt(43 i))/2 \$ and \$ (3 + sqrt(43i))/2 \$

C) \$ (3 + sqrt(43 i))/7 \$ and \$ (3 + sqrt(43i))/7 \$

D) \$ (2 + sqrt(43 i))/7 \$ and \$ (2 + sqrt(43i))/7 \$