1. ## Intermediate Value Theorem

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval:

1. the third root of x = 1-x, (0,1)

Note: I'd really appreciate it if somebody could tell me how to type in the square root and other root symbols.

2. cosx = x (0,1)

2. Originally Posted by dm10
Note: I'd really appreciate it if somebody could tell me how to type in the square root and other root symbols.
$\displaystyle \frac{2}{3}$

Code:
$\frac{2}{3}$
$\displaystyle 2\sqrt{32}$

Code:
$2\sqrt{32}$

Mo.

3. Originally Posted by dm10
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval:

1. the third root of x = 1-x, (0,1)

Note: I'd really appreciate it if somebody could tell me how to type in the square root and other root symbols.

2. cosx = x (0,1)
1. Use the function $\displaystyle f(x) = x^{1/3} + x - 1$, and calculate the values for this function at x = 0 and x = 1. What does the Intermediate Value Theorem tell you about this result?

2. Use the function $\displaystyle g(x) = \cos x - x$, calculate the value for this function at x = 0, and show that $\displaystyle \cos 1 - 1$ is negative.