Applied Mathematics - Continuity and Differentiability

Continuity and DifferentiabilityContinuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functionsConcept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functionsLogarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivativesRolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretationSUMMARY1.

A real valued function is continuous at a point in its domain if the limit of the function at that point equals the value of the function at that point. A function is continuous if it is continuous on the whole of its domain. 2.

Sum, difference, product and quotient of continuous functions are continuous. i. e.

, if f and g are continuous functions, then (f ± g) (x) = f (x) ± g(x) is continuous. (f. g) (x) = f (x).