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Section Solutions

Graphing

  1. parabola with vertex at \((0,-4)\text{,}\) y-intercept \((0,-4)\text{,}\) x-intercepts at \((\pm 2,0)\)

  2. rational function with horizontal asymptote \(y=1\) and vertical asymptote \(x=-2\)

  3. be sure you can graph all your trig functions and state their domains and ranges

  4. root functions look like half a parabola sideways, x-intercept \((2/3,0)\text{,}\) domain \([2/3, \infty)\)

  5. half parabola and half straight line, domain \((-\infty,\infty)\)

Evaluate the following limits or state why they do not exist.

  1. \(13\)

  2. \(-1\)

  3. \(-\frac{1}{4} \;\; \mbox{and} \;\; -4\)

  4. DNE since LHL = 2 doesn't equal RHL = -4

  5. DNE since LHL DNE (note that RHL = 0)

  6. \(3x+1\)

  7. \(\frac{1}{7}\)

  8. \(\frac{3}{2}\)

  9. limit does not exist; \(x=-1\) is a horizontal asymptote, so neither left nor right limits exist

  10. \(\frac{-1}{2\sqrt{3}}\)

  11. \(\sqrt{2}/2\) for all three answers

  12. \(4\) for all three answers

  13. \(-4x\)

  14. \(0\)

List the interval(s) on which each of the following is continuous.

  1. \((-\infty,-\frac{1}{3}), (-\frac{1}{3},\frac{1}{2}), (\frac{1}{2},\infty)\)

  2. \([-5,\infty)\)

  3. \((-\infty,\infty)\)

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

  5. \((-\infty,2), (2,\infty)\)

  6. continuous everywhere except \(\beta = \frac{(2k-1)\pi}{2}\) where k is an integer

  7. \((-\infty,\infty)\)

  8. all \(x\) except \(x=\pi\)

Velocity

  1. 16 ft/sec, \(3(p+q)+1\) ft/sec

  2. 8000 and 6000 ft/sec

Secant and Tangent Lines

  1. \(y = \frac{2}{\pi}x+1\)

  2. \(y=9x+2\)

  3. \(y= \frac{1}{4} x + \frac{9}{4}\)

  4. \(y = \frac{1}{6}x + \frac{5}{3}\)

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