Consider the expression Q(x)= x+7 -3 x^ 2 -4 with approaching .
MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
Consider the expression
Q(x)=x2−4x+7−3
with x approaching 2.
(1) Verify analytically that both the numerator and the denominator of Q(x) approach 0 as x→2. State the numerical value each approaches.
(2) 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.