Section 2.3 — Examples

Evaluate the limit, if it exists.

  1. \( \displaystyle \lim_{x\to 2} (x^3 - 3x^2 + 5) \)
  2. \( \displaystyle \lim_{x\to 3} \frac{x^2 - 9}{x - 3} \)
  3. \( \displaystyle \lim_{x\to \tfrac{\pi}{2}} \frac{\sin x}{\cos 2x} \)
  4. \( \displaystyle \lim_{x\to -3} \frac{x^3 - 2x^2 - 15x}{x^2 + x - 6} \)
  5. \( \displaystyle \lim_{t\to 1} \frac{t^2 + t - 2}{t^4 - 1} \)
  6. \( \displaystyle \lim_{h\to 0} \frac{\sqrt{16+h} - 4}{h} \)
  7. \( \displaystyle \lim_{u\to 4} \frac{\sqrt{2u+1} - 3}{u^2 - 4u} \)