Calculate and interpret average rates of change as secant slopes, and estimate instantaneous rates of change numerically and graphically as tangent slopes with appropriate signs and units. Evaluate finite and infinite one-sided and two-sided limits from graphs, tables, and algebraic expressions using substitution, factoring, canceling, or rationalizing, distinguishing limiting behavior from the value at the point. Identify removable, jump, and infinite discontinuities and relate the limit of difference quotients to instantaneous rate of change and the derivative when it exists, without formal $\varepsilon$-$\delta$ proofs or advanced generalizations.