Use the Intermediate Value Theorem to show that the following equations have solutions for 0 ≤ x ≤ 1.
1. ex + x2 - 2 = 0.
2. ex - 3x2 = 0.
3. ex + x2 - 2 = x.
4. ex + x2 - 2 = cos(2πx) - 1.
5. xe-3(x - 1) - 2 = 0 (you will need to check an intermediate point).
6. x3e-4(x - 1) - 1.1 = 0 (you will need to check an intermediate point).