MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
The function f is defined for all real numbers. A portion of its numerical values near x=3 is shown below.
x 2.900 2.990 2.999 3.001 3.010 3.100
f(x) 6.102 6.010 6.001 5.999 5.990 5.905
In addition, f(3)=7.
(a) Estimate x→3limf(x). Express your answer to three decimal places.
(b) Explain how the values in the table support your estimate in part (a). In your explanation, reference the behavior of f(x) as x approaches 3 from both the left and the right.
(c) Determine whether f is continuous at x=3. Justify your conclusion using the formal definition of continuity in terms of limits and function value.