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1. Find \(\lim_{x \rightarrow \infty} \frac{x - 2x^2}{3x^2 - 4x + 5}\).

a.  \(\frac{1}{2}\)

b.  \(-\frac{2}{3}\)

c.  \(\frac{1}{3}\)

d.  \(\frac{2}{3}\)

e.  \(0\)

For Questions 2, 3, and 4, let \(f(x) = \frac{1}{x^2 + 1}\)

2. Find the largest open interval(s) over which \(f\) is increasing.

a.  \((-\infty, 0)\)

b.  \((0, \infty)\)

c.  \((-\infty, \infty)\)

d.  \((-\infty, 1)\)

e.  \((-1, \infty)\)

3. Find the largest open interval(s) over which \(f\) is concave down.

a.  \((-\frac{1}{2}, \frac{1}{2})\)

b.  \((-\frac{1}{2}, \infty)\)

c.  \((-\infty, -\frac{1}{2}), (\frac{1}{2}, \infty)\)

d.  \((-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})\)

e.  \((-\frac{\sqrt{3}}{3}, \frac{\sqrt{3}}{3})\)

4. Find the horizontal asymptote for \(y = f(x)\).

a.  \(y = -1\)

b.  \(y = 0\)

c.  \(y = \frac{1}{2}\)

d.  \(y = 1\)

e.  There is no horizontal asymptote.