Question

If 3x − 5 ≤ f(x) ≤ x2 − 3x 4 for x ≥ 0, find lim x→3 f(x)

Answer 1

The limit as x approaches 3 of the given function is 4.

Step-by-step explanation:

To find the limit as x approaches 3 of the function f(x), we first need to evaluate the function at x = 3. Since the function is given as a range, we need to find the values of f(x) that satisfy the given inequality for x ≥ 0.

Plug in x = 3 into both sides of the inequality and evaluate:

3(3) - 5 ≤ f(3) ≤ 3^2 - 3(3) + 4

9 - 5 ≤ f(3) ≤ 9 - 9 + 4

4 ≤ f(3) ≤ 4

Since f(3) is always equal to 4, the limit as x approaches 3 of f(x) is also equal to 4.