For each pair of functions, say which approaches 0 more quickly as x approaches infinity. Explain which rule you used to compare each pair. Compute the value of each function at x = 1, x = 10, and x = 100. How do these compare with the order of the functions in the limit? If they are different, how large would x have to be for the values to match the order in the limit?
1. e-2x and x-10
2. 10e-x and 0.1e-0.2x
3. 1000/x and x-3.5
4. x-0.1 and 25x-0.2
5. x-2 and 30/ln(x)
6. l/ln(x) and 30x-0.1