Successive differentiation, Asymptotes, Multiple points, Tests for concavity and convexity, Points of inflexion, Tracing of curves in Cartesian, parametric and polar forms. Curvature, Radius of Curvature, Centre of Curvature.
Integration of hyperbolic and inverse hyperbolic functions, Reduction Formulae, Application of definite integral to find quadrature, Length of an arc, Improper integrals and their convergence, Comparison tests, Absolute and conditional convergence, Abel’s and Dirichlet’s tests. Frullani integral. Integral as a function of a parameter. Beta-Gamma Functions and their convergence.