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Problem 5 Score: /25 Consider the following graphs and write down the functions they represent. a...
Crown Academy 7. (8 points)(K(U), A) Determine which graphs represent polynomial functions. Explain how you know....
Crown Academy 7. (8 points)(K(U), A) Determine which graphs represent polynomial functions. Explain how you know. Write down the equation of the polynomial function and compare their graphs. (C1.4) a) c) -2 d) b)
(10 ea) For the following system transfer functions, draw the signal-flow graphs, write the Conce...
(10 ea) For the following system transfer functions, draw the signal-flow graphs, write the Concerning an open-loop version of the system above, write the state and output functions, and represent the systems in state space in Jordan canonical form. 3. (s+3)2 (s+4) G(s)=-(s+7) G(s) (s+4) s+ b) c) (s+2)2(s+5)(s+6)
(10 ea) For the following system transfer functions, draw the signal-flow graphs, write the Concerning an open-loop version of the system above, write the state and output functions, and represent the...
4. [25 POINTS]Use separate graphs to draw indifference curves for each of the following utility functions: (a) 6 POINTS...
4. [25 POINTS]Use separate graphs to draw indifference curves for each of the following utility functions: (a) 6 POINTS] U (x, y) = min{2x + y, 2y + x}. (b) [6 PoINts] U (x,y) = max{2.x + y, 2y + x}. (c) 6 POINTS] U (x,y) = x + min {x, y}. (d) 7 POINTS] In which of these cases are preferences convex?
4. [25 POINTS]Use separate graphs to draw indifference curves for each of the following utility functions: (a)...
Consider the following graphs of functions
Consider the following graphs of functions Which of the graphs represent functions where using local linearization to approximate the value of the function near the identified point will always give an under estimate? There may be more than one correct answer. A. h(x) B.f(x) C. I(x) D. g(x) E. None of the above Which graph(s) has a global minimum somewhere on the graph shown? There may be more than one correct answer. A. f(x) B. I(x) OC. h(x) D. g(x) E. None of the above Which graph(s) has a local extrema somewhere on the...
Problem 2 Score: /25 Identify all asymptotes for the following functions. Even if a function possesses...
Problem 2 Score: /25 Identify all asymptotes for the following functions. Even if a function possesses no asymptotes of a certain type, please state so explicitly (e.g, if f(x) for instance has no vertical asymptotes, please state this in your final answer). a (12 points): f(1) = (2-1)(3+3)
Problem 1. (25 points) Consider the following differential equation. 36 (a) Using the change of variable, 2 VT, write the differential equation in the form of Bessel's equation, 22y" zy(22- v...
Problem 1. (25 points) Consider the following differential equation. 36 (a) Using the change of variable, 2 VT, write the differential equation in the form of Bessel's equation, 22y" zy(22- v2)y 0. (b) Find the general solution of the differential equation (y(). (You do not need to find the value:s of Gamma functions.) (c) Find the term multiplying ? in the solution. (You do not need to find the values of Gamma functions.)
Problem 1. (25 points) Consider the following...
Q3 1. For the following, in (a) sketch the graphs of the functions and in (a)...
Q3
1. For the following, in (a) sketch the graphs of the functions and in (a) and (b) find the areas as indicated (a) the area bounded by y = f(x) = x2 - 4x + 5 and y = g(2) = 2x - 3. (b) the area of the region that is common to r= 3 cos(0) and r = sin(). See sketch below. 2. Consider the region bounded by y? = 4, y = 2 and r =...
question #5 (b) Suggest two distinct utility functions that represent such preterences. (Hint: Think about monotonic...
question #5
(b) Suggest two distinct utility functions that represent such preterences. (Hint: Think about monotonic transformations.) (c) Find MRS analytically. How does MRS depend on the values of (1, 72). Intuitively explain why (d) She spends her total income of $100 paying pi $2 for each Red Delicious and p2 $1 for each Gala. Find her optimal demand and show it on the graph. (e) Describe Kate's optimal choice(s) when p $1. Consumer Demand 5. For each of the...
2. [8 pts] Consider the region R enclosed by the graphs of functions f(x) = 2...
2. [8 pts] Consider the region R enclosed by the graphs of functions f(x) = 2 – 22 – 2x + 3 and g(x) = -2 +3 + 5 with points of intersection (-1,3) and (2,3), as shown in the figure. (a) Set up but do not evaluate the integral that repre- sents the volume of the solid resulting from revolving the region R about the vertical line r = 3. NA (b) Set up but do not evaluate the...
Problem 3 Consider a particle with total angular momentum quantum number l (1) Write down the...
Problem 3 Consider a particle with total angular momentum quantum number l (1) Write down the matrix L, representing L using the basis formed by {|l, m)], which are co-eigenstates of I2 and L. Choose the order of the basis vectors such that the diagonal matrix elements of L, are in descending order. [10 points] 2) Write down the matrix representations of L+ and L using the same basis for representing L. [20 points] (3) Write down the matrix representations...
Crown Academy 7. (8 points)(K(U), A) Determine which graphs represent polynomial functions. Explain how you know. Write down the equation of the polynomial function and compare their graphs. (C1.4) a) c) -2 d) b)
(10 ea) For the following system transfer functions, draw the signal-flow graphs, write the Concerning an open-loop version of the system above, write the state and output functions, and represent the systems in state space in Jordan canonical form. 3. (s+3)2 (s+4) G(s)=-(s+7) G(s) (s+4) s+ b) c) (s+2)2(s+5)(s+6)
(10 ea) For the following system transfer functions, draw the signal-flow graphs, write the Concerning an open-loop version of the system above, write the state and output functions, and represent the...
4. [25 POINTS]Use separate graphs to draw indifference curves for each of the following utility functions: (a) 6 POINTS] U (x, y) = min{2x + y, 2y + x}. (b) [6 PoINts] U (x,y) = max{2.x + y, 2y + x}. (c) 6 POINTS] U (x,y) = x + min {x, y}. (d) 7 POINTS] In which of these cases are preferences convex?
4. [25 POINTS]Use separate graphs to draw indifference curves for each of the following utility functions: (a)...
Problem 2 Score: /25 Identify all asymptotes for the following functions. Even if a function possesses no asymptotes of a certain type, please state so explicitly (e.g, if f(x) for instance has no vertical asymptotes, please state this in your final answer). a (12 points): f(1) = (2-1)(3+3)
Problem 1. (25 points) Consider the following differential equation. 36 (a) Using the change of variable, 2 VT, write the differential equation in the form of Bessel's equation, 22y" zy(22- v2)y 0. (b) Find the general solution of the differential equation (y(). (You do not need to find the value:s of Gamma functions.) (c) Find the term multiplying ? in the solution. (You do not need to find the values of Gamma functions.)
Problem 1. (25 points) Consider the following...
Q3
1. For the following, in (a) sketch the graphs of the functions and in (a) and (b) find the areas as indicated (a) the area bounded by y = f(x) = x2 - 4x + 5 and y = g(2) = 2x - 3. (b) the area of the region that is common to r= 3 cos(0) and r = sin(). See sketch below. 2. Consider the region bounded by y? = 4, y = 2 and r =...
question #5
(b) Suggest two distinct utility functions that represent such preterences. (Hint: Think about monotonic transformations.) (c) Find MRS analytically. How does MRS depend on the values of (1, 72). Intuitively explain why (d) She spends her total income of $100 paying pi $2 for each Red Delicious and p2 $1 for each Gala. Find her optimal demand and show it on the graph. (e) Describe Kate's optimal choice(s) when p $1. Consumer Demand 5. For each of the...
2. [8 pts] Consider the region R enclosed by the graphs of functions f(x) = 2 – 22 – 2x + 3 and g(x) = -2 +3 + 5 with points of intersection (-1,3) and (2,3), as shown in the figure. (a) Set up but do not evaluate the integral that repre- sents the volume of the solid resulting from revolving the region R about the vertical line r = 3. NA (b) Set up but do not evaluate the...
Problem 3 Consider a particle with total angular momentum quantum number l (1) Write down the matrix L, representing L using the basis formed by {|l, m)], which are co-eigenstates of I2 and L. Choose the order of the basis vectors such that the diagonal matrix elements of L, are in descending order. [10 points] 2) Write down the matrix representations of L+ and L using the same basis for representing L. [20 points] (3) Write down the matrix representations...
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