For each pair of functions, say which approaches infinity faster 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. x2 and e2x
2. x3 and l000x
3. x3.5 and 0.1x10
4. 5ex and e5x
5. 0.lx0.5 and 30 1n(x)
6. 10x0.1 and x0.5