Section6.3

# Section6.3 - Math 2B Dr C Famiglietti Section 6.3 The...

This preview shows pages 1–3. Sign up to view the full content.

Math 2 B Dr. C. Famiglietti ************************************************************************ Section 6.3: The Exponential Function The inverse of the natural logarithmic function (presented in Section 6.1) is the natural exponential function y = e x , where e 2.71828 Since the two are inverse functions, the graph of y = e x can be obtained from the graph of y = ln x by reflecting the graph of y = ln x about the line y = x . The graph of y = e x is shown here and has the following characteristics: Domain: −∞ , ( ) Range: 0, ( ) Increasing throughout its domain Concave upward Passes through 0,1 ( ) since e 0 = 1 lim x →∞ e x = lim x →−∞ e x = 0 . The graph of y = e x is a reflection of the graph of y = e x about the y-axis and is therefore, decreasing throughout its domain with lim x →∞ e x = 0 and lim x →−∞ e x = .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Properties of the natural exponential function, y = e x 1. e ln x = x , for x > 0 . 2. ln e x ( ) = x , for −∞ ≤ x ≤ ∞ . Derivative of the natural exponential function d dx e x ( ) = e x To derive the differentiation formula (without using the definition of the derivative) for
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

Section6.3 - Math 2B Dr C Famiglietti Section 6.3 The...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online