Figure 5.2 Each small line segment has a slope of 1

.x

Figure 5.5 e is the base for the natural logarithm because ln 1.e

Figure 5.12 The graph of1f is a reflection of the graph of f in the line .y x

Figure 5.13 If a horizontal line intersects the graph of f twice, then f is not one-to-one.

Figure 5.19 The inverse function of the natural logarithmic function is the natural exponential function.

Integrals of Hyperbolic Functions

Let u be a differentiable function of x.

Integration Involving Inverse Hyperbolic Functions

Let u be a differentiable function of x. (The following formulas are in logarithmic form.)