Consider the expression
Q(x)=x2−4x+7−3
with x approaching 2.
a. Verify analytically that both the numerator and the denominator of Q(x) approach 0 as x→2. State the numerical value each approaches.
b. Without performing the full algebraic simplification, explain in clear, complete sentences why a single algebraic manipulation cannot produce a finite limit for Q(x) at x=2. In your explanation, identify the distinct algebraic obstacles that must be removed and describe the sequence in which they must be addressed before substitution becomes legitimate.