Problem 4. (1p) (Book exercise 1.1.3) What is the relative error in rounding 4.9997 to 5.000?

Problem 5. (a: 2p, b: 2p, c: 4p, total 8p) (Book exercises 1.1.7, 1.4.9 and 1.4.19)

1. For small x which is the better way of evaluating (1+x)²: Directly as (1+x)² or as (x+2)x+1? Explain your choice.
2. How would you evaluate 1-cosx for x close to 0? Explain your approach.
3. Find a good way to compute sinx+cosx-1 for x near 0.

Problem 6 (3x2p = 6p). Use Horners rule to evaluate

1. P(x) = 2x⁴+9x²-16x+12 at x= -6
2. P(X) = 2x⁴-3x³-5x²+3x+8 at x=2
3. P(x) = 3x⁵-38x³+5x²-1 at x=4