2. Theory of the Derivative 2.1 Tangent Lines 2.2 Definition of - PowerPoint PPT Presentation

May 31, 2023 •25 likes •1.08k views

2. Theory of the Derivative 2.1 Tangent Lines 2.2 Definition of Derivative 2.3 Rates of Change 2.4 Derivative Rules 2.5 Higher Order Derivatives 2.6 Implicit Differentiation 2.7 LHpitals Rule 2.8 Some Classic Theoretical Results

sin( x ) Compute lim x → 0 x
cos( x ) Compute lim x → 0 x
2.8 Some Classic Theoretical Results
• This is not a course in theory, but certain results are important for the CLEP. • Proving these would be an excellent learning experience, but is certainly not necessary. A basic understanding would suffice for the CLEP exam.
Differentiability Implies Continuity Suppose a function f is di ff erentiable at a point x. Then f is continuous at x.
Rolle’s Theorem Suppose a function f is di ff erentiable on an interval ( a, b ) . If f ( a ) = f ( b ) , then there is a point c, a < c < b such that f 0 ( c ) = 0 .

Download Presentation

Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Existence of tangent lines to sub-Riemannian geodesics joint with R. Monti and A. Pigati Davide

Sub-Riemannian geodesics Proof of the theorem Existence of tangent lines to sub-Riemannian geodesics joint with R. Monti and A. Pigati Davide Vittone Universit di Padova Workshop on Geometric Measure Theory Warwick, July 11th, 2017

507 views • 26 slides

Derivative Applications MAC 2233 Instantaneous Rates of Change of a Function The derivative

3/16/2010 Derivative Applications MAC 2233 Instantaneous Rates of Change of a Function The derivative is: The slope of the tangent line at a point The instantaneous rate of change of the function Marginal Analysis The study

561 views • 18 slides

From Math 2220 Class 6 Tangent Lines Planes in R 3 Lines in R 3 Dr. Allen Back Cross product

From Math 2220 Class 6 V1c Chain Rule Tangent Planes From Math 2220 Class 6 Tangent Lines Planes in R 3 Lines in R 3 Dr. Allen Back Cross product Sep. 10, 2014 Chain Rule The chain rule in multivariable calculus is in some ways very

892 views • 67 slides

Geometric Interpretation of the Derivative (Review) Geometric Interpretation of the Derivative

Geometric Interpretation of the Derivative (Review) Geometric Interpretation of the Derivative (Review) The derivative of a function f ( x ) at point x 0 is the slope of the tangent line at that point. Geometric Interpretation of the Derivative

550 views • 32 slides

Connections in Tangent Categories Robin Cockett University of Calgary (joint work with Geoff

Connections in Tangent Categories Connections in Tangent Categories Robin Cockett University of Calgary (joint work with Geoff Cruttwell) Category Theory 2016 Dalhousie Connections in Tangent Categories Tangent categories The basics

807 views • 41 slides

Electric field lines Imaginary lines or curves drawn through a region of space such that their

Electric field lines Imaginary lines or curves drawn through a region of space such that their tangent at any point are in the direction of the electric field vector at that point Electric field lines (cont.) Higher density of lines

796 views • 9 slides

Differential structure, tangent structure, and SDG Geoff Cruttwell (joint work with Robin

Introduction Tangent structure Tangent spaces Representable tangent structure Conclusion Differential structure, tangent structure, and SDG Geoff Cruttwell (joint work with Robin Cockett) In honour of Robin Cocketts 60th birthday FMCS

755 views • 58 slides

SHANNONS INFORMATION THEORY ITS APPLICATIONS IN DERIVATIVE PRICING ALEXANDER KUSHPEL AND

SHANNONS INFORMATION THEORY ITS APPLICATIONS IN DERIVATIVE PRICING ALEXANDER KUSHPEL AND JEREMY LEVESLEY Abstract. During the past two decades Lvy processes became very popular in Financial Mathematics. Truncated Lvy distributions were

656 views • 16 slides

Equivariant K -theory and tangent spaces to Schubert varieties William Graham and Victor Kreiman

Equivariant K -theory and tangent spaces to Schubert varieties William Graham and Victor Kreiman Flag varieties Notation G = simple algebraic group B = Borel subgroup, B = opposite Borel subgroup T = maximal torus contained in B

431 views • 18 slides

Calculus without Limits: Trigonometry the Theory The derivative Fundamental A Critique of the

Calculus without Limits C. K. Raju Outline Calculus without Limits: Trigonometry the Theory The derivative Fundamental A Critique of the History of Mathematics theorem of calculus Functions The New Pedagogy Zeroism Conclusions

1.9k views • 162 slides

Weil spaces and closed tangent structure June 2, 2018 1 / 30 Overview W 1 -actegories

Weil spaces and closed tangent structure June 2, 2018 1 / 30 Overview W 1 -actegories Tangent categories 1 W 1 -presheaf cats 2 Embedding theorem Closed and representable tangent categories 3 2 / 30 Tangent categories and Weil

559 views • 32 slides

MATH 12002 - CALCULUS I 2.1: Derivative and Slope Examples Professor Donald L. White

MATH 12002 - CALCULUS I 2.1: Derivative and Slope Examples Professor Donald L. White Department of Mathematical Sciences Kent State University D.L. White (Kent State University) 1 / 8 Examples Example Find the equation of the tangent line

310 views • 8 slides

Parallel lines They are lines whose distance between then does not change along their

D AY 4 P ARALLEL LINES I NTRODUCTION We see electric cables hanging between poles, athletic track lines and so many other similar features. Have we ever asked ourselves about a special feature about the lines that are identified with these

348 views • 12 slides

u t = u t u t d u = u u + u u d t = u A Vectors Derivative is

Vector Derivative expressed in terms of its smoothly varying (time dependent) magnitude & direction (unit vector) functions. u t = u t u t d u = u u + u u d t = u A Vectors Derivative is determined by its current

662 views • 11 slides

Tangent estimation along 3D digital curves l Postolski 1 , 2 , Marcin Janaszewski 2 , Yukiko

Introduction Discrete Straight Segments -Maximal Segment Tangent Direction Experimental Validation Tangent estimation along 3D digital curves l Postolski 1 , 2 , Marcin Janaszewski 2 , Yukiko Kenmochi 1 , Micha Jacques-Olivier Lachaud 3 1

613 views • 26 slides

Derivative Function Math 132 Stewart 2.2 In Notes 2.1, we defined the derivative of a

Derivative Function Math 132 Stewart 2.2 In Notes 2.1, we defined the derivative of a function f ( x ) at x = a , namely the number f ( a ). Since this gives an output f ( a ) for any input a , the derivative defines a function.

176 views • 5 slides

1 Canny Edge Detection Steps: 1. Apply derivative of Gaussian 2. Non-maximum suppression

Edge and Corner Detection What causes an edge? Reading: Chapter 8 (skip 8.1) Goal: Identify sudden changes

342 views • 5 slides

CS 4495 Computer Vision Linear Filtering 2: Templates, Edges Aaron Bobick School of Interactive

Templates/Edges CS 4495 Computer Vision A. Bobick CS 4495 Computer Vision Linear Filtering 2: Templates, Edges Aaron Bobick School of Interactive Computing Templates/Edges CS 4495 Computer Vision A. Bobick Last time: Convolution

1.01k views • 59 slides

Topic 10 Polynomial a + bx + cx 2 can be represented by the Example: Symbolic list (+ a (+

Symbolic differentiation Topic 10 Polynomial a + bx + cx 2 can be represented by the Example: Symbolic list (+ a (+ (* b x) (* c (* x x)))) Differentiation Derivative with respect to x is b + 2cx, which can be represented by (+

255 views • 3 slides

2 3 SessionID 4 5 A. B. C. D. 6 A. B. C. D. 7 8 9 10 11 A. B. C. D. 12 A.

2 3 SessionID 4 5 A. B. C. D. 6 A. B. C. D. 7 8 9 10 11 A. B. C. D. 12 A. B. C. D. 13 14 15 16

636 views • 20 slides

END-TO-END DIFFERENTIABLE PHYSICS FOR LEARNING AND CONTROL Filipe de Avila Belbute-Peres 1 Kevin

END-TO-END DIFFERENTIABLE PHYSICS FOR LEARNING AND CONTROL Filipe de Avila Belbute-Peres 1 Kevin Smith 2 Kelsey Allen 2 Joshua Tenenbaum 2 Zico Kolter 13 1 School of Computer Science, Carnegie Mellon University 2 Brain and Cognitive Sciences,

629 views • 10 slides

On Implicit Image Derivatives and Their Applications Alexander Belyaev Mohamed Omran Uni

Introduction Background From Explicit to Implicit Differentiation Schemes Discussion On Implicit Image Derivatives and Their Applications Alexander Belyaev Mohamed Omran Uni Saarland Milestones and Advances in Image Analysis, 2012 1 / 32

487 views • 35 slides

Numerical Differentiation & Integration Composite Numerical Integration I Numerical Analysis

Numerical Differentiation & Integration Composite Numerical Integration I Numerical Analysis (9th Edition) R L Burden & J D Faires Beamer Presentation Slides prepared by John Carroll Dublin City University c 2011 Brooks/Cole,

1.14k views • 93 slides

Some Notes on Automatic Differentiation Chih-Jen Lin National Taiwan University Last updated:

Some Notes on Automatic Differentiation Chih-Jen Lin National Taiwan University Last updated: May 25, 2020 Chih-Jen Lin (National Taiwan Univ.) 1 / 13 Here we give some notes on the slides at https://www.cs.toronto.edu/~rgrosse/courses/

176 views • 13 slides