textbook-theory · English
Limits And The Notion Of Continuity
Section 2.3 of Dan Sloughter's open calculus text 'Difference Equations to Differential Equations,' covering the formal definition of limits for real-valued functions, one-sided limits, limits at infinity, and the notion of continuity. The section introduces the Heaviside function and piecewise examples to illustrate discontinuities, derives limit laws for polynomials and rational functions, and treats vertical and horizontal asymptotes via limit notation. Eighteen pages of exposition and problems are included.
limitscontinuitycalculusreal analysis