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[DOC File]Section 1
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The expression is the average rate of change of f(x) on the closed interval [a, x]. Thus, is the instantaneous rate of change of y = f(x) at x = a. In particular, if y = f(x) is the position of an object at time x, is the average velocity and is the instantaneous velocity at x = a. Examples: 1.
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[DOC File]Tangent Lines and Rates of Change
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(such as the average velocity) The average rate of change of over the time interval is the slope of the secant line to the points and on the graph (Figure 2). Instantaneous Rate of Change. The instantaneous rate of change of at the time is the slope of the tangent line …
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[DOC File]Calculus II - MATH
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A common application in calculus focuses on the relationships among the position, velocity, and acceleration of some object. If we know the position of the object according to some function rule—revealed through a symbolic representation or a table of values or a graphical representation—then the derivative of the position function ...
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[DOC File]Section 1
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Average velocity over [a, b] is ; Instantaneous velocity at time t is defined as . v(t) = s’(t) ... Examples: A small balloon is released at a point 150 feet away from an observer, who is on level ground. ... AP Calculus Chapter 3: Differentiation Rules Stewart.
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[DOC File]Integration of discrete function
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The upward velocity of a rocket is given as a function of time in Table 1. Table 1. Velocity as a function of time. 0 0 10 227.04 15 362.78 20 517.35 22.5 602.97 30 901.67 Determine the distance, covered by the rocket from to using the velocity data provided and use any applicable numerical technique. Solution. Method 1: Average Velocity Method
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[DOC File]Pennsylvania State University
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Calculus is traditionally divided into two branches, differential calculus and integral calculus. ... Average Velocity of an Object in Rectilinear Motion. ... Compare the calculations in Examples 1.1 and 1.3. Can the average velocity of an object in rectilinear motion over a time interval always be represented as the slope of a secant line on ...
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[DOC File]Velocity/Acceleration Worksheets - mrbartonsclassroom
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Velocity/Acceleration Worksheets. Calculating Average Speed. Graph the following data on the grid below and answer the questions at the bottom of the page. SHOW WORK! Time (sec) Distance (m) 0 50 75 90 110 125 What is the average speed after two seconds? After three seconds? After 5 seconds? What is the average speed between two and four minutes?
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[DOC File]MAT 271 - Arizona State University
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Jul 13, 2008 · For the given position functions calculate average velocity. a) b) c) For the given position functions calculate instantaneous velocity. a) b) c) Section 2.2 The Derivative. Definition: The derivative of the function at is defined as provided the limit exists. If this limit exists we say that is differentiable at .
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[DOCX File]Calculus Review 3 - University of Delaware
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Velocity = speed times direction (constant times a unit direction vector) Distance between 2 points = magnitude of vector from one to other. Point midway between 2 points = “average” of their 2 position vectors . 2. Inner products and cross products. ... Examples: torque, angular velocity. Torque (Moment)
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[DOC File]Average Rate of Change vs
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Average rate of change- secant line. Instantaneous rate of change- tangent line. If I drive down the shore, and it takes me 2 hours to go 80 miles- what is my average velocity? That is my average rate of change or secant line; At what speed was I driving at exactly 15 minutes into the trip- that is my instantaneous velocity or tangent line ...
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Average velocity calculus examples