The document applies the Intermediate Value Theorem to demonstrate that there is a root for the equation cos(x) = e^x - 2 within the interval (0, 1). It defines the function f(x) = cos(x) - e^x + 2 and evaluates it at the endpoints f(0) = 2 and f(1) = -0.18, indicating a sign change. According to the theorem, since the function is continuous and changes signs, a root exists in this interval.

1. Use the Intermediate Value Theorem to show that there is a root of the equation in the given
interval. cos = ex - 2, (0, 1)
Solution
f(x)= cos x -e^x +2
f(0)= 2
f(1)= -0.18
Since the function is continuous in the interval and changes signs the intermediate value
theormem says there will be a root in the interval.