Learning Paths
Each learning path is one chapter: a guided route through a topic, one small course at a time. Pick a class to see its chapters in order.
Chapter 20
Limits and Derivatives
A car shows 60 km/h on the dial, yet it never drives for a single instant. How can a speed exist at one moment? The answer is a limit. This chapter starts with the idea of a limit, learns to find limits by algebra and by the standard limits, and then uses a limit to define the derivative: the slope of a tangent and the rate of change at an instant. You differentiate polynomials and trigonometric functions from first principles and with the product and quotient rules. The last course takes the harder limits that exams love, with the number e, the squeeze theorem, series expansions and L'Hôpital's rule. It covers the unit of the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level, IB and AP. Python checks the numbers.
3 courses
