Calculus I: Limits & Derivatives+50 
Calculus I: Limits & Derivatives introduces foundational concepts in calculus, focusing on understanding how functions behave as inputs approach specific values (limits) and how to calculate instantaneous rates of change (derivatives). The course covers techniques for evaluating limits, rules for differentiation, and applications such as finding slopes of curves and solving real-world problems involving motion and change. Mastery of these topics is essential for further study in mathematics, science, and engineering.
Calculus I: Limits & Derivatives+50
Calculus I: Limits & Derivatives introduces foundational concepts in calculus, focusing on understanding how functions behave as inputs approach specific values (limits) and how to calculate instantaneous rates of change (derivatives). The course covers techniques for evaluating limits, rules for differentiation, and applications such as finding slopes of curves and solving real-world problems involving motion and change. Mastery of these topics is essential for further study in mathematics, science, and engineering.
💡 Key Takeaways
- Understand the concept of a limit and what a function value approaches as x nears a point or infinity
- Use limit techniques (algebraic manipulation, factoring, rationalizing, and the squeeze theorem) to evaluate limits
- Define and interpret the derivative as the instantaneous rate of change and the slope of a tangent line
- Differentiate common functions using derivative rules (power, product, quotient, and chain rule)
❓ Frequently Asked Questions
What is a limit?
The value f(x) approaches as x gets arbitrarily close to a (x → a); it may or may not equal f(a).
How do you evaluate a limit that can't be substituted directly?
Use algebraic techniques (factoring, canceling common factors, rationalizing) and known limit rules; check one-sided limits if needed.
What is a derivative?
The instantaneous rate of change of f at x; the slope of the tangent line. It’s defined as f'(x) = lim_{h→0} [f(x+h) - f(x)]/h.
What is the chain rule?
If y = f(g(x)), then dy/dx = f'(g(x)) · g'(x).
What is the difference between a limit and a derivative?
A limit describes the value a function approaches near a point, while a derivative is a specific limit that gives the rate of change at a point.