Homework 04 due 20 February 2017

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Complete the following problems and upload your solutions to the D2L dropbox by 5:00 PM on Monday, 20 February 2017.

1. (5 points) Use the bisect function to find the positive root of

   $$3.06 = \frac{(1-x)\sqrt{3+x}}{x\sqrt{1+x}}$$

2. (7 points) Use the bisect function to find the four roots of

   $$\mathrm{sin}(\theta^2) = 0.09 + 2\theta - \theta^2$$

3. (8 points) Use the bisect function to find the first five positive roots of

$$1 - z\,\mathrm{cot}(z) = \mathrm{Bi}$$

for $\mathrm{Bi}=5$.

Hint: For some problems you may need to adjust the convergence tolerance to avoid the warning message from bisect.