For all x=2, a function f is defined analytically by
f(x)=∣x−2∣(x+3)(x2−4)(x−5).
Answer the following related questions.
(a) Calculate x→2−limf(x). Show all algebraic steps and clearly indicate how you address any indeterminate forms.
(b) Calculate x→2+limf(x), providing complete justification of each manipulation.
(c) Does x→2limf(x) exist? State your conclusion and support it using the results from parts (a) and (b).
(d) Classify the type of discontinuity that f exhibits at x=2 and justify your classification with reference to both the one-sided limits and the explicit form of f(x).