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For questions 1 through 3, compute the antiderivatives.

1. \(\int 3x + 4 dx\)

a.  \(3 + c\)

b.  \(3x^2 + 4x + c\)

c.  \(\frac{3}{2}x^2 + 4x + c\)

d.  \(3x^2 + 2x + c\)

d.  \(\frac{3}{2}x^2 + 2x + c\)

2. \(\int (x + 1)(x + 2) dx\). (Hint: before you start taking a derivative, try a little algebra.)

a.  \((\frac{1}{2}x^2 + x)(\frac{1}{2}x^2 + 2x) + c\)

b.  \((\frac{1}{2}x^2 + 2x)(\frac{1}{2}x^2 + 4x) + c\)

c.  \(2x + 3 + c\)

d.  \(\frac{1}{3}x^3 + \frac{3}{2}x^2 + 2x + c\)

d.  \(\frac{2}{3}x^3 + 3 x^2 + 2x + c\)

3. \(\int 3\sin x - \sec^2 x dx\).

a.  \(3\cos x - \frac{1}{3} sec^3 x + c\)

b.  \(-3\cos x - \frac{1}{3} sec^3 x + c\)

c.  \(3\cos x - \tan x + c\)

d.  \(-3\cos x - \tan x + c\)

d.  \(cos^3 x - \tan x + c\)

4. Evaluate the sum \(\sum_{k=-4}^{4} x^3\).

a.  0

b.  10

c.  100

d.  200

e.  201

5. Which of the following is equivalent to the sum \(1 + 10 + 100 + 1000 + 10000\)?

a.  \(\sum_{n = 1}^10000 n\)

b.  \(\sum_{n = 0}^10000 n\)

c.  \(\sum_{n = 1}^4 10^n\)

d.  \(\sum_{n = 0}^4 10^n\)

e.  \(\sum_{n = 1}^4 10n\)

For questions 6 and 7, say a hot air balloon starts at an altitude of 100 m and is initially falling at a rate of 2 m/s. At time 0, the balloon operator fires the burner and the balloon accelerates upwards at a rate of 1 m/s\(^2\).

6. Find a formula for the vertical velocity, \(v\) of the balloon in m/s.

a.  \(v(t) = 2t + 100\)

b.  \(v(t) = t + 100\)

c.  \(v(t) = t - 2\)

d.  \(v(t) = 2t - 2\)

e.  \(v(t) = 2t - 1\)

7. Find a formula for the height, \(h\) of the balloon in m.

a.  \(h(t) = t^2 + 100t\)

b.  \(h(t) = \frac{1}{2}t^2 + 100t + 100\)

c.  \(h(t) = \frac{1}{2}t^2 + t + 100\)

d.  \(h(t) = \frac{1}{2}t^2 - t + 100\)

e.  \(h(t) = \frac{1}{2}t^2 - 2t + 100\)