Taking the derivative of e
[DOC File]New Chapter 3
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By taking the derivative, we can find a formula for the slope of a line tangent to any point of f : In particular, the slope of the tangent line of f at x = 1 is . By using the point-slope formula of the line equation with slope 2 and the point (1, 1), we have. The graph of and the tangent line at x = 1 can be seen in Figure 5.1. (Figure 5.1
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[DOC File]AP Calculus Assignments: Derivative Techniques
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Review the two limit definitions of the derivative f '(a). 9. Kenny was given the function y = xlnx for x ( [1, e] and asked to find the rate of change of y with respect to x.
[DOC File]Derivatives - UH
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The derivative is a calculated quantity that tells you the slope of the tangent line to any point on the graph. The definition of a derivative is taking a limit as h approaches zero, but we’ll use the shortcuts to find them. This is the instantaneous rate of change of the graph at a chosen point.
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The verb “differentiate” a function means to “take derivative” of that function with respect to its variable. For instance, if C denotes a cost function, then its marginal cost is the first derivative of the cost function, i.e., You can also take a second derivative,
[DOC File]PART III
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Marginal revenue is found by taking the first derivative of total revenue with respect to Q or: Similarly, marginal cost is determined by taking the first derivative of the total cost function with respect to Q or: Equating MC and MR to determine the profit-maximizing quantity, 55 - 4Q = 2Q - 5, or.
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[DOC File]The Directional Derivative
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Instructor: Andrew Spieker Time/Place: TBA. Seminar Abstract. So, z = a + bi, where i is the solution to the equation x2 = –1. Sure, so what does that mean? Why do we care? In this seminar, we introduce the motivation behind complex numbers, and lead into a discussion about the algebra of complex variables; this will set us up to discuss the complex plane as a vector space of “equal shape ...
[DOC File]Kinematics Multiples - Travellin
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e. * A. Since you are going from velocity to position, you are working backwards, or taking the integral. If you chose graph B, you were taking the derivative. The velocity graph can be broken down into three regions: in the first region, the particle moves with constant positive speed so the position graph is linear with positive slope.
[DOC File]Problem Set #8
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E[U(Y)] = .25 ln(9,000) +.75 ln(10,000) = 9.184. b. Suppose that Ms. Fogg can buy insurance against losing the $1000 (say, by purchasing traveler’s checks) at an “actuarially fair” premium of $250. Show that her expected utility is higher if she purchases this insurance than if she faces the chance of losing the $1000 without insurance.
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