e^x and ln x
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Lesson Description:
Early Transcendental extra video lecture including exponentials and the natural logarithm.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
Additional Resources:
- Derivatives and Integrals of exponential and natural logarithm functions - A list of derivatives and integrals of the exponential and natural logarithm function.
Questions answered by this video:
- What is e?
- What is the limit definition of the number e?
- What are the properties of e^x?
- What is the derivative of e^x?
- What is ln x?
- How are e^x and ln x related?
- What are the properties of ln x?
- What is the change of base formula for logarithms and why does it work?
- What is logarithmic differentiation?
- What is the derivative of x^-x?
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Staff Review
This video explains what the number e is, what the limit definition of e is, and what e^x looks like and acts like. Some really high-level proofs are explained in this video. These might be above the level of an ordinary Calculus student. The number e and the exponential function e^x are used to explain ln x, or log base e of x. Properties of logs are explained using rules of exponents.
