1 / 7

Understanding Logarithmic and Exponential Functions in Calculus II

Explore the critical concepts of logarithmic and exponential functions as covered in Calculus II. This lesson focuses on the graphs of y = b^x for different bases b, the inverse relations between these functions, and methods of solving logarithmic and exponential equations. We also delve into the derivative of exponential functions using logarithmic differentiation and introduce the exponential integral, emphasizing the power rule. Gain a deeper understanding of these fundamental mathematical concepts and their applications.

berg
Télécharger la présentation

Understanding Logarithmic and Exponential Functions in Calculus II

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 7.3 Logarithmic and Exponential Functions Math 6B Calculus II

  2. Exponential Functions • The graph of y =bx, where b > 1 • The graph of y =bx, where 0 < b < 1

  3. Inverse Relations for Exponential and Logarithmic Functions • For any base b > 0, with , the following inverse relation hold. • Solving Logarithmic and Exponential Equations.

  4. The Derivative of bx • We will use logarithmic differentiation to find dy/dx where y = bx • The end resultwe get is:

  5. Exponential Integral • Exponential Integral of bx:

  6. The Power Rule • If n is any real number and f (x) = xn, then f ‘(x) = nxn-1

  7. The Evolution of logbx

More Related