Consider the following equation. cos x = x3 (a) Prove that the equation has at least one real root. f(x) = cos x − x3 is continu
ous on the interval [0, 1], f(0) = 0, and f(1) = cos 1 − 1 ≈ −0.46 0. Since 0 −0.46, there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation cos x − x3 = , or cos x = x3, in the interval (0, 1). (b) Use your calculator to find an interval of length 0.01 that contains a root.
1 answer:
You might be interested in
First, find the mean. You'll need it to compute the variance.
The variance of the sample is then computed with the formula
The standard deviation is the square root of the variance, so
The variance of the sample is then computed with the formula
The standard deviation is the square root of the variance, so