Answer: For the function f(x) = cos(x) + cos(2x) - 1 with ε ≤ 0.01:
To find where the function stays within ε of 0, you need to solve the inequality |f(x)| ≤ ε.
So, |cos(x) + cos(2x) - 1| ≤ 0.01.
2. For the function f(x) = x^5 + 3x^3 - 6x + 2 with & ≤ 0.01:
Similar to the first question, to find where the function stays within & of 0, solve |f(x)| ≤ &.
This results in |x^5 + 3x^3 - 6x + 2| ≤ 0.01.
By solving these inequalities, you can determine the intervals of x values where the functions remain within ε and & of 0 respectively. Remember to apply the absolute value to the function expressions and then solve the inequalities to find the x values satisfying the conditions given.
Step-by-step explanation:
