Verify the given linear approximation at
a = 0.
Then determine the values of x for which the linear approximation is accurate to within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places.)
To verify a linear approximation at a = 0, we need to have the equation of the linear function and the function for which the approximation is being made. Without these equations, it is not possible to fully answer your question.
However, I can provide you with the general steps to determine the values of x for which the linear approximation is accurate to within 0.1. Here's how you can do it:
1. Find the equation of the linear function: A linear approximation takes the form f(x) = f(a) + f'(a)(x - a), where f'(a) is the derivative of the function evaluated at a.
2. Determine the function for which the linear approximation is being made.
3. Set up the inequality |f(x) - L(x)| ≤ 0.1, where L(x) is the linear approximation from step 1.
4. Solve the inequality to find the values of x that satisfy the condition. This may involve simplifying the expression and using algebraic techniques. The resulting intervals will be the values of x for which the linear approximation is accurate to within 0.1.
Please provide the specific equations involved so that I can assist you further in solving the problem.