Numerade

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The transition to parenthood is less difficult when husband and wife share work based on O a traditional ideology. O an egalitarian ideology. O a similar ideology. O a dissimilar ideology.

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D) (3 points) Write an equation of the tangent line to the graph $y = 1 + \frac{4}{1 + e^{-2x}}$ at the point with $x = 0$. E) (4 points) Estimate the value of $1 + \frac{4}{1 + e^{-0.02}}$ using the linear approximation to $f(x)$ at $a = 0$.

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4. Suppose there is first-order difference equation of the following form: $2x_t - 4x_{t-1} = 6\theta_t$, where $x_t$ is endogenous and $\theta_t$ is exogenous. Suppose that $x_0 = 0$ and that $\theta_0 = 0$. Suppose that, starting in period 1, $\theta_t$ rises to 1 and remains equal to 1 in all future periods. Find the path that $x_t$ follows over time. Remember to find both the general solution and the particular solution. The value of c in the general solution can be obtained from the initial conditions.

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Problem (1) f(t) 1 0 f(t) = t² for 0 < t ? 1, and so on periodically 1 2 t 3 4 Calculate the Fourier expansion parameters of f(t): $a_0$, $a_n$, $b_n$ Useful integrals: $\int x^2 \sin ax \, dx = \frac{2x}{a^2} \sin ax + \frac{2 - a^2x^2}{a^3} \cos ax$ $\int x^2 \cos ax \, dx = \frac{2x}{a^2} \cos ax + \frac{a^2x^2 - 2}{a^3} \sin ax$

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Determine the angular velocity of the disk when $t = 2$ t starts from rest. 0.5 m N G 40

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1. You are given the circuit shown below. a) Find an expression for the transfer function $V_{out}(s)/V_{in}(s)$ in terms of s,R, L, and C. b) The circuit has the following component values: R = 10k?, C = 0.1?F, and L = 195.45?H and you are told that input voltage has the form: $V_{IN}(t) = 10 \cos(\omega t) + 3.33 \cos(3\omega t) + 2 \cos(5\omega t)$ Assuming that f = 36kHz, what is the expression for the output voltage? c) Is this a low-pass or high-pass filter? Explain using your answer form part b. + $V_{IN}$ L 2. You are given the circuit shown below $i_g$ 50 k? $i_o(t)$ + $v_o(t)$ 0.5 µF a) Determine the transfer function $I_o(s)/I_g(s)$. What are the pole and zero frequencies in both rad/sec and Hz? b) Determine the transfer function $V_o(s)/I_g(s)$. What are the pole and zero frequencies in both rad/sec and Hz? c) Sketch the Bode plot magnitude for $I_o(s)/I_g(s)$. Your y-axis should be in dB. Your x-axis should be in rad/sec. d) Sketch the Bode plot magnitude for $V_o(s)/I_g(s)$. Your y-axis should be in dB. Your x-axis should be in rad/sec.

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Consider the following differential equation: $\frac{dy}{dx} = \sin(xy^2)$ a. Use the MATLAB routine ode45 to generate approximate solutions to this di\nerential equation over the interval $-2 \le x \le 3$ first with initial condition $y(-1) = 0$ and then with initial condition $y(-1) = 1$. b. Graph the two computed solutions on the same set of axes using the following formatting instructions. • Create a title that contains your name and describes the graph (something like "Numerical Solutions of $\frac{dy}{dx} = \cos(xy^2)$ by I. M. Smart") obviously your real name! • Be sure to label your axes. The only variables in the problem are $x$ and $y$. Don't use other letters in your axis labels. • Include a date/time stamp.

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The table below gives the labor productivity of Grapeland and Scotland in liters per hour: Wine Grapeland Scotland Whisky 3,000 5,000 1,000 10,000 A) Which country has the absolute advantage in wine? In Whisky? B) Which country has a comparative advantage in Whisky? C) What are the upper and lower bounds for the trade price of Whisky? D) If the two countries decide to trade 100 liters of Whisky at a rate of 2 liters of wine per liter of whisky, what are the gains from trade?

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The following table shows the supply and demand for loanable funds schedule in a small island country in the Caribbean at the beginning of 2016. By the end of the year however, the demand for loanable funds increases by $2 billion at each level of the real interest rate and the supply of loanable funds increased by $1 billion at each interest rate. Predict the conditions of the loanable funds market in this country, under the following two scenarios: Scenario 1 and Scenario II. Demand for (percent per year) loanable funds loanable funds Real interest rate Supply of (billions of 2009 dollars per year) 4 8.5 5.5 5 8.0 6.0 6 7.5 6.5 7 7.0 7.0 8 6.5 7.5 9 6.0 8.0 10 5.5 8.5 a. Scenario 1. The government budget has neither a surplus nor a deficit during the year. Under this scenario, the real equilibrium interest rate by the end of the year will be billion; private investment will be $ percent; the quantity of private saving will be $ b. Scenario 2. The government budget deficit reaches $1 billion. Under this scenario, the real interest rate would be private saving would be $ billion. percent; the quantity of private investment would be $ billion. Assuming no Ricardo-Barro effect, there would be crowding out of $ billion, and the quantity of million private investment.

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Which of the following statements about manufacturers is true? Multiple Choice Industrial customers are concentrated in countries that are at the more advanced stages of economic development Manufacturing output in the U.S. is shrinking Countries with cheap labor have a slow rate of growth Many factories are concentrated in rural areas of the United States Currently, U.S. manufacturing output is at its lowest point since 1980

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gregory r.