Chapter 1.1, Problem 2ES

Show that the following equations have at least one solution in the given intervals.

1. a. $\sqrt{x}$ − cos x = 0, [0, 1]
2. b. e^x − x² + 3x − 2 = 0, [0, 1]
3. c. −3 tan(2x) + x = 0, [0, 1]
4. d. ln x − x² + $\frac{5}{2}x$ − 1 = 0, $\left[\frac{1}{2},1\right]$