Download presentation

Presentation is loading. Please wait.

Published byBrendan Hodge Modified over 4 years ago

1

EXPONENTIAL FUNCTIONS: DIFFERENTIATION AND INTEGRATION

Section 5.4

2

When you are done with your homework, you will be able to…

Develop properties of the natural exponential function Differentiate natural exponential functions Integrate natural exponential functions

3

Definition of the Natural Exponential Function

The inverse function of the natural logarithmic function is called the natural exponential function and is denoted by That is,

4

The inverse relationship between the natural logarithmic function and the natural exponential function can be summarized as follows:

5

Solve 6.0 0.0

6

Solve All of the above. B and C

7

Solve. Round to the nearest ten thousandth.

0.680 0.0001

8

Theorem: Operations with Exponential Functions

Let a and b be any real numbers.

9

Properties of the Natural Exponential Function

The domain is all real numbers and the range is all positive real numbers The natural exponential function is continuous, increasing, and one-to-one on its entire domain. The graph of the natural exponential function is concave upward on its entire domain. The limit as x approaches negative infinity is 0 and the limit as x approaches positive infinity is infinity.

10

Theorem: Derivative of the Natural Exponential Function

Let u be a differentiable function of x.

11

Find the derivative of

12

Find the derivative of

13

Find the derivative of

14

Theorem: Integration Rules for Exponential Functions

15

Evaluate

16

Evaluate

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.