'Continuous functions' diaporamas de présentation

PARTIAL DERIVATIVES

14. PARTIAL DERIVATIVES. PARTIAL DERIVATIVES. One of the most important ideas in single-variable calculus is: As we zoom in toward a point on the graph of a differentiable function, the graph becomes indistinguishable from its tangent line.

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Differentiation-Continuous Functions

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Differentiation-Continuous Functions

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Evaluating Limits Analytically

Evaluating Limits Analytically. Section 1.3. After this lesson, you will be able to:. evaluate a limit using the properties of limits develop and use a strategy for finding limits evaluate a limit using dividing out and rationalizing techniques. Limits ? Analytically.

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What you will learn

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Calculus and Analytical Geometry

Lecture # 6. Calculus and Analytical Geometry. MTH 104. Limits at Infinity. If the values of a variable x increases without bound, then we write. and if the values of x decreases without bound, then we write. For example.

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Section 16.7

Section 16.7. Triple Integrals. TRIPLE INTEGRAL OVER A BOX. Consider a function w = f ( x , y , z ) of three variables defined on the box B given by

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The Fundamental Group

The Fundamental Group. Sam Kitchin. Definitions. A path is a continuous function over the interval [0,1] in a space X A loop is a path that starts and ends at the same point, x 0 , called the base point of the loop. Examples of Loops. Homotopy.

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Continuity

Continuity. What is continuity? Algebraic properties Compositions. Definition. A function f is continuous at x=c if f(c) is defined lim x ?c f(x) exits lim x ?c f(x) = f(c) If one of these fails to hold, say that f is discontinuous at c. Examples.

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Ch 6.1: Definition of Laplace Transform

Ch 6.1: Definition of Laplace Transform. Many practical engineering problems involve mechanical or electrical systems acted upon by discontinuous or impulsive forcing terms. For such problems the methods described in Chapter 3 are difficult to apply.

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2.3 continuity

2.3 continuity. Definition: Continuity At A Point. Interior point: a function is continuous at an interior point c of its domain if . Endpoint: a function is continuous at a left endpoint a or is continuous at a right endpoint b of its domain if or respectively.

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Area Bounded by Curves

Area Bounded by Curves. sin x. cos x. Area Bounded by Curves (Integrating w.r.t. x ). Let f and g be continuous functions. Let R be the region bounded above by y = g ( x ), below by y = f ( x ), on the left by x = a and on the right by x = b . Then R has area. ?.

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2.3 Continuity

2.3 Continuity. Photo by Vickie Kelly, 2002. Greg Kelly, Hanford High School, Richland, Washington. Grand Canyon, Arizona. 2. 1. 1. 2. 3. 4.

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MAT 171 Precalculus Algebra Section 9-7 Parametric Equations

MAT 171 Precalculus Algebra Section 9-7 Parametric Equations. Cape Fear Community College Dr. Claude S. Moore. 9.7 Parametric Equations. Graph parametric equations. Determine an equivalent rectangular equation for parametric equations.

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7.8 Improper Integrals

7.8 Improper Integrals. Definition: The definite integral is called an improper integral if At least one of the limits of integration is infinite, or The integrand f ( x ) has one or more points of discontinuity on the interval [ a , b ]. Infinite Limits of Integration.

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Continuity and End Behavior of Polynomials

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2-3 continuity

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Improper Integrals

Improper Integrals. Infinite Integrand Integrand is unbounded at some point on the interval of integration. Infinite Interval One or both of the limits of integration are infinite Lower limit of ??. Upper limit of ?. The Big Question. Is an improper integral convergent or divergent?

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