Continuity and Differentiability — Chapter Summary

A function is continuous at

A function is continuous at a point c if the limit of the function at c equals the function value at c. In symbols, \lim_{x \to c} f(x) = f(c). This m

A function is continuous if it

A function is continuous if it is continuous at every point of its domain. For a closed interval [a,b], continuity at the endpoints is checked using o

If a function is not continuous

If a function is not continuous at c, it is discontinuous at c, and c is called a point of discontinuity.

Sum

Sum, difference, product, and quotient of continuous functions are continuous, provided the denominator in a quotient is nonzero. Composition of conti

The derivative at c is defined

The derivative at c is defined by the limit of the difference quotient if that limit exists. A function is differentiable at a point when this limit e