Calculus and Differeential Equations - MADE EASY Study Material for GATE, ESE and SES Exams

Latest:

Definite Integrals

If ∫ab f(x)dx = [F(x)]ab = F(b) – F(a) is called the definite integral of f(x) between the limits of

We study three areas where applications of integration is applied 1. Areas of curves 2. Length of curves 3. Volumes

There are two areas where derivatives are used 1. Increasing and Decreasing Functions 2. Maxima and Minima Relative maxima and

Rolle’s Theorem If a function f (x) is such that: f (x) is continuous in the closed interval a ≤

Theorem: If a function is differentiable at any point, then it is necessarily continuous at that point; proof of this

Derivative at a point: Let I denote the open interval (a, b) in R, and let x₀ ∈ I. Then

Definition of Continuity A function f(x) is defined for x = a is said to be continuous at x =

Definition A number A is said to be limit of a function f(x) at x = a if for any