This document is an 18-page review on limits, continuity, and the definition of the derivative in calculus. It begins with formal definitions of the derivative of a function, the derivative at a point, and continuity. It then provides examples and practice problems related to evaluating limits, including as x approaches infinity or a number, and limits related to continuity and derivatives. The document concludes with several free response questions involving analyzing functions for continuity and differentiability over an interval. In summary, this review covers key calculus concepts of limits, continuity, and the definition of the derivative through formal definitions, examples, and practice problems.
This is a simple PowerPoint on the properties of Sine and Cosine functions. It was created for a student teaching lesson that I had in the past. Feel free to use and modify! :-)
Polynomial Function and Synthetic DivisionAleczQ1414
This file is about Polynomial Function and Synthetic Division. A project passed to Mrs. Marissa De Ocampo. Submitted by Group 6 of Grade 10-Galilei of Caloocan National Science and Technology High School '15-'16
This is a simple PowerPoint on the properties of Sine and Cosine functions. It was created for a student teaching lesson that I had in the past. Feel free to use and modify! :-)
Polynomial Function and Synthetic DivisionAleczQ1414
This file is about Polynomial Function and Synthetic Division. A project passed to Mrs. Marissa De Ocampo. Submitted by Group 6 of Grade 10-Galilei of Caloocan National Science and Technology High School '15-'16
Image sciences, image processing, image restoration, photo manipulation. Image and videos representation. Digital versus analog imagery. Quantization and sampling. Sources and models of noises in digital CCD imagery: photon, thermal and readout noises. Sources and models of blurs. Convolutions and point spread functions. Overview of other standard models, problems and tasks: salt-and-pepper and impulse noises, half toning, inpainting, super-resolution, compressed sensing, high dynamic range imagery, demosaicing. Short introduction to other types of imagery: SAR, Sonar, ultrasound, CT and MRI. Linear and ill-posed restoration problems.
Lesson 14: Derivatives of Logarithmic and Exponential Functions (slides)Matthew Leingang
The exponential function is pretty much the only function whose derivative is itself. The derivative of the natural logarithm function is also beautiful as it fills in an important gap. Finally, the technique of logarithmic differentiation allows us to find derivatives without the product rule.
Lesson 14: Derivatives of Logarithmic and Exponential Functions (slides)Mel Anthony Pepito
The exponential function is pretty much the only function whose derivative is itself. The derivative of the natural logarithm function is also beautiful as it fills in an important gap. Finally, the technique of logarithmic differentiation allows us to find derivatives without the product rule.
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Understanding the "Chain Rule" for Derivatives by Deriving Your Own VersionJames Smith
Because the Chain Rule can confuse students as much as it helps them solve real problems, we put ourselves in the shoes of the mathematicians who derived it, so that students may understand the motivation for the rule; its limitations; and why textbooks present it in its customary form. We begin by finding the derivative of sin2x without using the Chain Rule. That exercise, having shown that even a comparatively simple compound function can be bothersome to differentiate using the definition of the derivative as a limit, provides the motivation for developing our own formula for the derivative of the general compound function g[f(x)]. In the course of that development, we see why the function f must be continuous at any value of x to which the formula is applied. We finish by comparing our formula to that which is commonly given.