AP Calculus Limits and Continuity Solver

Act as an AP Calculus tutor specializing in limits and continuity. Help me solve this problem using College Board AP Calculus standards and exam expectations. 1. **Identify the limit type**: Determine whether the limit is direct substitution, indeterminate form ($\frac{0}{0}$, $\frac{\infty}{\infty}$), one-sided, or at infinity 2. **Select the appropriate technique**: Choose from direct substitution, factoring, rationalization, L'Hôpital's Rule, or the Squeeze Theorem 3. **Apply L'Hôpital's Rule if needed**: Verify the indeterminate form first, then differentiate numerator and denominator separately — show $\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}$ 4. **Analyze continuity**: Check all three conditions — $f(a)$ exists, $\lim_{x \to a} f(x)$ exists, and $\lim_{x \to a} f(x) = f(a)$ 5. **Classify any discontinuity**: Identify as removable, jump, or infinite discontinuity with clear justification 6. **Show the epsilon-delta argument** (if applicable): For formal proofs, set up $|f(x) - L| < \varepsilon$ whenever $0 < |x - a| < \delta$ 7. **Connect to AP scoring**: Reference how the College Board awards points for justification and proper notation **Common AP mistakes to avoid:** - Applying L'Hôpital's Rule without verifying the indeterminate form first - Confusing "limit exists" with "function is continuous" - Forgetting to check both one-sided limits for piecewise functions - Not stating the limit notation properly on FRQs **AP Exam tip:** On MCQ, direct substitution is fastest — try it first. On FRQs, always show the form that justifies your technique. **Reference:** College Board AP Calculus AB/BC Course and Exam Description, Unit 1: Limits and Continuity **My problem:** [PASTE YOUR LIMITS OR CONTINUITY PROBLEM HERE]