1. The first exercise is to find the various partials of CE (S, t) in order to obtain abetter sense of how changes in variable affect its value.(a) Find aC (S,1). What does this partial mean should r increase? Should rdecrease?(b) FindдаCE(S.1). What does this partial mean should the value of o increase?(The market is more volatile.) Should o decrease? (The market calms down.)(c) Find aC (S.1)Ət

To determine: ∂CEs,t∂r,and find out partial mean should r increase? Should r decrease? ∂CEs,t∂σ,…

Answered: The first exercise is to find the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The slope of a regression equation indicates: A. the magnitude of the residual prior to squaring B. where the regression line will cross the x-axis C. where the regression line will cross the y-axis D. the marginal change in the y value for every one unit change in the x value E. the marginal change in the x value for every one unit change in the y value F. where the regression line will go through the point (x-bar, y-bar)
13 14 16 E3 f7 esc %24 4 & %23 3 tab W E R T Y OM EWORK 4 ution 2.2: # 22 Find the derivative of the fundtion ucing the definition of derivative. State the domain of the function and the domain of its derivative. f(x) = 4+ 8x -5x2 %3D 6 2)
2. Consider the three functions below: S(x) = 2r S(z) =r S(z) = 2 (a) Create a t-table for cach of the three functions, using the x-values-2, -1, 0, 1, 2, and 3. (b) Which function appears to be growing the fastest? That is, for which function are the y-values increasing the fastest? (c) On the same set of axes, graph all three of the functions above. Be sure to scale your axes! Was your answer to part b correct?
3.4.5
15. Let a be a real number. We will explore the derivatives of the function f(x) = eax. By using the chain rule, we see (a) What is Recall that the second derivative of a function is the derivative of the deriva- tive function. Similarly, the third derivative is the derivative of the second derivative. (b) What is d² dx² d3 C030 BY NO SA d dx = aeax (eax), the third derivative of eax? (c) Let n be a natural number. Make a conjecture about the nth derivative dn of the function f (x) = eax. That is, what is (eax)? This con- dxn jecture should be written as a self-contained proposition including an appropriate quantifier. (eax), the second derivative of eax? 4.1. The Principle of Mathematical Induction (d) Use mathematical induction to prove your conjecture. 183
2. As ultrasound propagates into the body, absorption and scattering result in a decrease (or attenu- ation) of the intensity. This can be described by the attenuation coefficient, a. In an experiment to investigate this attenuation in the chest wall of humans, measurements were conducted in which the attenuation of ultrasound through sample human tissue was measured as a function of the ultrasound frequency, f [1]. (a) The figure below (adapted from [1]) shows a set of measurements of the attenuation coef- ficient as a function of the frequency. Fit a linear function to the data points shown. You should draw an approximate line of best fit, determine the slope and intercept of your fit, and then quote the final equation for your line. 12 10 2 1 3 4 5 Frequency (MHz) Attenuation coefficient (dB/cm)

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