Mathematics

Mathematics

Problem

## End of Chapter 3 Drill The answers are in Chapter 24. 2. Evaluate lim⁡x→2x2−x−2x2−8x+15\lim _{x \rightarrow 2} \frac{x^{2}-x-2}{x^{2}-8 x+15}. (A) 0 (B) 23\frac{2}{3} (C) 3 (D) The limit does not exist. (A) 0 (B) 23\frac{2}{3} (C) 3 (D) The limit does not exist.
Intuitive explanation

When you substitute x=2x = 2 directly into this rational function, you get a real number in both numerator and denominator—not an indeterminate form like 00\frac{0}{0}. This means you can evaluate the limit by simple substitution without needing to factor or simplify. Just plug in and compute carefully.

Intuitive explanation

When you substitute x=2x = 2 directly into this rational function, you get a real number in both numerator and denominator—not an indeterminate form like 00\frac{0}{0}. This means you can evaluate the limit by simple substitution without needing to factor or simplify. Just plug in and compute carefully.

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