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Problem 32. Use the four-step process to determine $f'(x)$ and then find $f'(1), f'(2), f'(3)$.\n$f(x) = -x^2 + 3x + 2$

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Subtract. \[ \begin{array}{l} -2-7= \\ 5-10= \end{array} \]

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A mutual fund sold $50 million of assets during the year and purchased $67 million in assets. If the average daily assets of the fund were $145 million, what was the fund turnover?

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Question Given the function $f(x) = -x - 2$, find the total area between $f(x)$ and the $x$-axis over the interval $[-5, -1]$.

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A 1.4-kg particle is moving in a potential field presented by the graph below. The parameters of the field are $V_0$ = 14.5 J, $V_1$ = 10 J, $x_1$ = 4 m, $x_2$ = 12 m, and $x_3$ = 20 m. If the total energy of the particle is $E_1$ = 9 J, what is the position of the left turning point and what is the speed of the particle as x = 8 m? $V_0$ $E_1$ $-V_1$ $x$ 0 $x_1$ $x_2$ $x_3$ $E_2$ The left turning point, $x_{L1}$ = 0.9 Units m The speed, $v_1$ = Units Select an answer If the speed of the particle is $v_2$ = 2.2 m/s at x = 8 m, what is the total energy of this particle? For this energy find the positions of the left and right turning points. The energy, $E_2$ = Units Select an answer The left turning point, $x_{L2}$ = Units Select an answer The right turning point, $x_{R2}$ = Units Select an answer

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The derivative of a function of $f$ at $x$ is given by $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$ provided the limit exists. Use the definition of the derivative to find the derivative of $f(x) = 4x^2 + 5x + 5$. Enter the fully simplified expression for $f(x+h) - f(x)$. Do not factor. $f(x+h) - f(x) = $ $f'(x) = $

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Our examples in the chapter have focused on manufacturing, where the output is units of product and the inputs are manufacturing activities or costs. The concept of productivity can be applied in a variety of settings, wherever there are inputs and outputs. For example, consider LandscapeCity, a landscape design company that specializes in small landscape projects for people living in cities. Amanda Caldwell, the assistant manager, is in the process of trying to determine if productivity has been improving since she was hired 6 months ago. Because it is a design firm, labor is the only significant expense, but Amanda is unsure if the number of projects or the dollar of sales volume should be used when computing productivity. She has collected these data for sales and labor expenses for the past 6 months: Labor Month Expense Number of Projects Sales Dollars 1 $ 16,470 34 $ 20,090 2 19,200 40 21,900 3 19,392 50 28,780 4 13,194 13 18,560 5 13,926 18 21,680 6 20,592 50 21,520 Required: 1. Calculate the productivity for each month and the change in productivity from month to month using number of projects as the measure of output. 2. Calculate the productivity for each month and the change in productivity from month to month using sales dollars as the measure of output. Complete this question by entering your answers in the tabs below. Required 1 Required 2 Calculate the productivity for each month and the change in productivity from month to month using number of projects as the measure of output. (Round your answers to 4 decimal places. Negative amounts should be indicated by a minus sign.).

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Home_work_2.pdf 0000 Microsoft Word - Home work 2.docx Frictionless $x_1(t)$ $x_2(t)$ 3- Find the state-space representation in phase-variable form for each of the systems shown in Figure P3.8. Repeat using MATLAB R(s) $\frac{100}{s^4 + 20s^3 + 10s^2 + 7s + 100}$ C(s) (a) R(s) $\frac{30}{s^5 + 8s^4 + 9s^3 + 6s^2 + s + 30}$ C(s) (b) 1 of 1 Find the transfer function $G(s) = Y(s)/R(s)$ for each of the following systems represented in state

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2. Determine the reactions at the pin and roller for the beam shown. 100 lb/ft 300 lb

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III. Find the Fourier series of $f(x)$, assume a period of $2\pi$. 6. $f(x) = |x|$

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