Consider the function
f(x)=⎩⎨⎧x−1x2−1,3,x=1,x=1.
Use the information below to analyze the behavior of f near x=1.
a. Part 1: Calculate x→1limf(x), showing all algebraic steps.
b. Part 2: Explain in complete sentences why the value obtained in part (a) is consistent with simplifying the expression for f(x) when x=1. In your explanation, reference the formal definition of a limit.
c. Part 3: Determine whether f is continuous at x=1 and justify your conclusion.