Find the derivative of \$g(z) = 4z^7 - 3z^(-7) + 9z\$.

A) \$g(z) = 28z^6 + 21z^(-8) + 9\$

B) \$g(z) = 28z^6 - 21z^(-8) - 10\$

C) \$g(z) = 28z^6 + 21z^(-8) + 15\$

D) \$g(z) = 28z^7 + 21z^(-7) + 9\$

Evaluate: \$ \int (3x^3 + 2)^5 x^2 dx \$.

A) \$ (1/54)(3x^3)^6 + C \$

B) \$ (1/14)(3x^3 + 2)^6 + C \$

C) \$ (1/54)(3x^3 + 2)^5 + C \$

D) \$ (1/54)(3x^3 + 2)^6 + C \$

Compute the sum of the first five terms of the sequence defined by an = 5n + 1.

A) 100

B) 80

C) 90

D) 70

Perform the indicated operation and write your answer in standard form (-3 - 9i)(1 + 10i).

A) (7 + 28i)

B) (7 - 28i)

C) (87 - 39i)

D) (39 - 28i)

Given the function, y is defined implicitly by the equation: \$ (x^2y + e^xy) = sin(x + y) \$.find \$dy / dx\$ at the point where x = 0 and y = 0.

A) 1

B) - 3

C) 2

D) - 1

Find the derivative of \$y = 2t^4 - 10t^2 + 13t\$.

A) \$dy / dt = 8t^3 - 20t - 15\$

B) \$dy / dt = 8t^2 + 20t + 13\$

C) \$dy / dt = 8t^3 - 20t + 13\$

D) \$dy / dt = 8t^3 - 20t + 19\$

Find the antiderivative of \$6e^2x\$.

A) \$3e^2 x^2 + C\$

B) \$4e^3 x^3/2 + C\$

C) \$3e^2 + x^2 + C\$

D) \$3e^2 - x^2 + C\$

Write out the first 3 terms of the harmonic series \$ \sum_{n=1}^\infty ​1/n \$​.

A) 1, 0.1, 0.3332

B) 1, 0.5, 0.3333

C) 0, 0.5, 0.3231

D) 1, 0.2, 0.3114

Solve \$ z^2 + 4z + 13\$ = 0 where z is a complex number.

A) (- 3 + 2i) and (- 3 - 2i)

B) (3 - 2i) and (3 + 2i)

C) (- 2 + 3i) and (- 2 - 3i)

D) (- 1 + 2i) and (1 + 2i)

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\$