## CS 4365/CS 5354 Data Processing Under Security and Privacy Summer 2016, Test 1

Name: __________________________________________________________

1. Similarly to how we used Newton's method to design algorithms for computing square root and cubic root, design an algorithm for computing the logarithm x = ln(a) as a solution to the equation

ex = a.

2. Use the algorithm for computing 1/b that we had in class (and that is implemented in the computers) to perform the few first steps of computing the ratio 1 / 1.1.

3-6.

3. Use numerical differentiation to compute the derivative of the function x2 − x when x = 1.

4. Use linearization technique and your estimate for the derivative to estimate the range of this function when x is in the interval [0.9, 1.1].

5. Use naive interval computations to estimate the same range.

6. Use mean value form to estimate the same range.

7. Use Newton's method to solve the following system of non-linear equations:
x1 * x2 = 3, x1 + x2 = 4.
Start with the first approximation x1 = 1 and x2 = 2. One iteration is good enough.

8. Find the point closest the origin on the line x1 − x2 = 1. In other words, find the values x1 and x2 for which the sum (x1)2 + (x2)2 attains the smallest possible value under the constraint x1 − x2 = 1.

9. Explain what is k-anonymity, and why it is important. If k increases, will we get more or less privacy protection? Explain your answer.