Abstract
This chapter reviews limits and derivatives. A limit plays a central role in calculus and in much of modern mathematics. Limits can be either infinite limits or limits at infinity. The limits i → ± ∞ of rational expressions can be found by first dividing the numerator and denominator by the highest power of x that appears in the denominator and then calculating the limit x →∞ (or - ∞) of both the numerator and denominator. The derivative is a fundamental tool of calculus or studying the behavior of functions of a real variable. The concept of continuity is one of the central notions in mathematics; a function is continuous at a point if it is defined at that point and if its graph moves unbroken through that point.
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