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

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

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

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

D) \$ y = 2x − ((10π)/3) ​+2\sqrt(5) \$

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

A) 5sec u + C

B) sec u + C

C) 5sin u + C

D) sin u + C

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

A) 6750

B) 6500

C) 5550

D) 6560

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

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

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

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

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

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

A) Converges, and its limit is 0.

B) Diverges

C) Not diverges

D) Invalid

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

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

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

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

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

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

A) \$x^3 + 2x^2 − 5x\$

B) \$x^3 + 2x^2 − 5x + 7 + C\$

C) \$x^3 + 2x^2 − 5x + C\$

D) \$x^3 + 2x^2 − 5x - C\$

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

A) \$ pi^8/90\$

B) \$ pi^4/80\$

C) \$ pi^8/80\$

D) \$ pi^4/90\$

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

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

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

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

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

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

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

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

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

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