Lecture 5 limit laws
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This document discusses various limit laws and techniques for calculating limits, including: 1) Using limit laws and graphs to evaluate specific limits, such as the product law 2) Limits involving indeterminate forms like 0/0 cannot always be directly substituted and may require alternative techniques 3) Other techniques include factoring, rationalizing fractions, and applying laws for powers, roots, and other specific limits.
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ch02edited is best for university students
This document outlines key concepts from a chapter on limits and continuity in calculus. It begins with an intuitive introduction to the limit process, providing examples to illustrate one-sided limits, limits that do not exist, and limits approaching infinity. It then defines the formal epsilon-delta definition of a limit. The document continues with sections on properties of limits, continuity, and theorems related to limits and continuity, such as the intermediate value theorem.
thses are best for college and university students
This document outlines key concepts from a chapter on limits and continuity in calculus. It begins with an intuitive introduction to limits, including examples of how limits are used to define concepts like slope, area, and length. It discusses one-sided limits and limits that do not exist. The document then provides the formal epsilon-delta definition of a limit and discusses properties of limits. It covers continuity, types of discontinuity, and theorems related to limits and continuity. Finally, it discusses specific limits involving trigonometric and other functions.
ch02edited.ppt
This document outlines key concepts from a chapter on limits and continuity in calculus. It begins with an intuitive introduction to the limit process, providing examples to illustrate one-sided limits, limits that do not exist, and limits approaching infinity. It then defines the formal epsilon-delta definition of a limit. The document continues with sections on properties of limits, continuity, and theorems related to limits and continuity, such as the intermediate value theorem.
ch02edited.ppt
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Lar calc10 ch04_sec5
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3) The General Power Rule - A common substitution that involves quantities raised to a power in the integrand.
It also covers evaluating definite integrals using substitution and recognizing when an integrand is an even or odd function to simplify the evaluation.
CALCULUS chapter number one presentation
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Lesson 1 - Introduction to Limits.pptx
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Chap4_Sec4 (1).ppt
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Lar calc10 ch05_sec1
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Week 6
The document discusses differentiation rules for various functions. It begins by discussing the derivatives of polynomials and exponential functions. The power rule is introduced, which states the derivative of x^n is nx^{n-1}. It then covers the derivatives of exponential functions f(x)=ax, proving the formula f'(x)=af(x). The product rule and quotient rule are also introduced. Finally, it discusses the derivatives of trigonometric functions, proving that the derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x).
Lar calc10 ch03_sec5
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Lar calc10 ch01_sec4
This document discusses continuity and one-sided limits of functions. It defines continuity at a point and on an open interval. Functions can have removable or nonremovable discontinuities. One-sided limits are used to investigate continuity on closed intervals. The intermediate value theorem guarantees that a continuous function takes on all intermediate values between its values at the endpoints of a closed interval. Examples demonstrate determining continuity and applying properties of continuity and the intermediate value theorem.
Guia limite
En este archivo se muestran las consideraciones preliminares para entender limites, tal como factorización, racionalización y valor absoluto. El tema es iniciado con la definición intuitiva, los diferentes teoremas que se aplican en límites, la indeterminación 0/0 y los diversos ejemplos al respecto
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Chapter 4 Applications of Differentiation James Stewart
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thses are best for college and university students
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- 1. Calculating Limits Using 2.3 the Limit Laws
- 2. Calculating Limits Using the Limit Laws 2
- 3. 3 Example 1 Use the Limit Laws and the graphs of f and g in Figure 1 to evaluate the following limits, if they exist. Figure 1
- 4. 4 Example 1(a) – Solution From the graphs of f and g we see that and Therefore we have = 1 + 5(–1) = –4 (by Law 1) (by Law 3)
- 5. cont’d 5 Example 1(b) – Solution We see that limx®1 f (x) = 2. But limx®1 g(x) does not exist because the left and right limits are different: So we can’t use Law 4 for the desired limit. But we can use Law 4 for the one-sided limits: The left and right limits aren’t equal, so limx®1 [f (x)g(x)] does not exist.
- 6. 6 Example 1(c) – Solution The graphs show that and Because the limit of the denominator is 0, we can’t use Law 5. The given limit does not exist because the denominator approaches 0 while the numerator approaches a nonzero number. cont’d Figure 1
- 7. 7 Power Law If we use the Product Law repeatedly with g(x) = f (x), we obtain the following law. Power Law
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- 15. 15 Finding Limits - Rationalization
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