Limits and Derivatives — Class 11 Mathematics

This chapter introduces calculus, the study of change. Starting from average velocities of a falling body, it builds an intuitive idea of the derivative as an instantaneous rate of change. The limit is the value approaches as approaches ; it exists only when the left-hand limit and right-hand limit coincide. Algebra of limits lets the limit of a sum, difference, product or quotient be computed from the limits of the parts; for polynomials and rational functions the limit is found by substitution (where the denominator is non-zero). Two standard trigonometric limits are and . The derivative of at is defined from first principles as . The algebra of derivatives gives sum, difference, product and quotient rules, and yields standard results such as , and .