Question

Find the limit L if L = lim(5x – 4). Then find the largest value o > 0 such that |f(x) – 4| < 0.01 whenever 0 < |x - 2| < o.

Answer 1

To find the limit L of the function 5x - 4, substitute x with positive or negative infinity. The limit is L = -4. Any positive value of o satisfies the condition |f(x) - 4| < 0.01 whenever 0 < |x - 2| < o.

Step-by-step explanation:

To find the limit L of the function 5x - 4, we substitute x with the value it approaches. Since there is no constraint on x, we substitute it with positive or negative infinity. Therefore, the limit is L = -4.

To find the largest value o > 0 such that |f(x) - 4| < 0.01 whenever 0 < |x - 2| < o, we need to determine the range of f(x) for 0 < |x - 2| < o. Since f(x) is a linear function, its range is unrestricted. Therefore, any positive value of o satisfies the given condition.