Maths · Class 11 · Chapter 12
Limits and Derivatives
12 lessons 93 min 2 simulations
This chapter opens calculus. The speed of a falling body at one instant cannot be read off as distance over time, so it is chased by averages over shorter and shorter intervals, and that chase is made exact by the idea of a limit. One-sided limits decide when a limit exists, limit rules and factor-cancelling handle polynomial and rational functions, a standard power limit and the sandwich theorem give the key trigonometric limit sin x/x → 1. The derivative is then defined as a limit of chord slopes, found from first principles, and turned into fast rules for sums, products, quotients, powers, polynomials and trigonometric functions.
What the exam asks
For JEE Main this is the doorway to all later calculus. Questions test 0/0 limits by factorising, the power limit naⁿ⁻¹, the limits sin x/x and tan x/x, left and right hand limits of piecewise functions, first-principles derivatives and the product and quotient rules. Most slips come from cancelling a factor that does not vanish, using degrees instead of radians, reversing the order in the quotient rule and treating f(a) as the limit.
Lessons
12 lessons · 93 min
1From average speed to instant speedNCERT §12.1, §12.2, Tables 12.1 to 12.312 min 1 sim2The idea of a limitNCERT §12.37 min3Left and right hand limitsNCERT §12.311 min 1 sim4Algebra of limitsNCERT §12.3.1, Theorem 16 min5Limits of polynomials and rational functionsNCERT §12.3.2, Examples 1 and 27 min6A standard limit for powersNCERT §12.3.2, Theorem 2, Example 37 min7Limits of trigonometric functionsNCERT §12.4, Theorems 3 to 5, Example 47 min8Derivative at a pointNCERT §12.5, Definition 1, Examples 5 to 86 min9Derivative from first principlesNCERT §12.5, Definition 2, Examples 9 to 126 min10Rules for derivativesNCERT §12.5.1, Theorems 5 and 6 (derivative rules)6 min11Derivatives of polynomials and trigonometric functionsNCERT §12.5.2, Theorem 7, Examples 13 to 227 min12Chapter reviewMust-know facts, traps and formulas11 min