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(2x) 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) ...

1 Let fx e x x 2 2 Then f0 1 0 and f1 e 1 0 By the Intermediate Value Theorem there must be a soluti ...

Use the Intermediate Value Theorem to show that the following equations have solutions for 0 x

Question:

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).