Homework Answers
Add Answer to:
Problem 2 Consider the system of equations 2 1. Show that the z and t are determined as a functio...
4. Consider the system of equations rey - ye?w = 1 +vw and usin(EU) = w...
4. Consider the system of equations rey - ye?w = 1 +vw and usin(EU) = w sin(yw). du Using the implicit function theorem, show that (x, y) can be expressed as a differ- entiable function of (vw) near (v, w) = (0,1). Find the values of (u, w) = (0,1). Be sure to show work. and
Please solve Q 7 & 8 7. 14+6 marks] Consider the initial value problem y_y2, 2,y(1) = 1 y'= 1-t (a) Assuming y(t) is bounded on [1, 2], Show that f(t,v)--satisfies Lipschitz condition with...
Please solve Q 7 & 8
7. 14+6 marks] Consider the initial value problem y_y2, 2,y(1) = 1 y'= 1-t (a) Assuming y(t) is bounded on [1, 2], Show that f(t,v)--satisfies Lipschitz condition with respect to y. (b) Use second order Taylor method with h 0.2 to approximate y(1.2), then use the Runge- Kutta method: to compute an approximation of y(1.4). 8. [4 marks) Assuming that a1, o2 are non negative constants, determine the parameters o and β1 of the...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given ...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
The Implicit Function Theorem and the Marginal Rate of Substitution (4 Points) 3 An important result...
The Implicit Function Theorem and the Marginal Rate of Substitution (4 Points) 3 An important result from multivariable calculus is the implicit function theorem which states that given a function f (x,y), the derivative of y with respect to a is given by where of/bx denotes the partial derivative of f with respect to a and af/ay denotes the partial derivative of f with respect to y. Simply stated, a partial derivative of a multivariable function is the derivative of...
1. Consider the system 2(t)--3i(t) +z2(t) +3() (a) (i) Find the linearised system at the equilibrium point (0, 0)....
1. Consider the system 2(t)--3i(t) +z2(t) +3() (a) (i) Find the linearised system at the equilibrium point (0, 0). (ii) What type of equilibrium point is (0,0)? (State your reasons fully.) (ii) Sketch the phase portrait for the linearised system near (0,0). (b) Repeat part (a) for the equilibrium point at (1,0). (c) (i) Are there any other equilibria? (ii) Read the Grobman-Hartman theorem and confirm that it applies to the above equilibria.
1. Consider the system 2(t)--3i(t) +z2(t) +3()...
5. Consider the nonlinear two dimensional Lotka-Volterra (predator-prey) system z'(t) = z(t)[2-2(...
5. Consider the nonlinear two dimensional Lotka-Volterra (predator-prey) system z'(t) = z(t)[2-2(t)-2y(t)l, y'(t) = y(t)12-y(t)--2(t)] (a) Find all critical points of this system, and at each determine whether or not the system is locally stable or unstable. (b) We proved in class, using the Bendixson-Dulac theorem, that this system has no periodic solution with trajectory in the first quadrant of the plane. Assuming this, use the Poincare-Bendixson theorem to prove that all trajectories (z(t),y(t)) of the system (2) with initial...
GROUP WORK 1, SECTION 14.3 Clarifying Clairaut's Theorem Consider f (x, y, z) = x?cos (y...
GROUP WORK 1, SECTION 14.3 Clarifying Clairaut's Theorem Consider f (x, y, z) = x?cos (y + 2). 1. Why do we know that fyyxxx=0 without doing any computation? 2. Do we also know, without doing any computation, that Sxyz = 0? Why or why not? 3. Suppose that a = 3x + ay". Jy = bxy + 2y. S,(1, 1) = 3, and has continuous mixed second partial derivatives xy and fyx. (a) Find values for a and b...
72 Partial Derivatives: Problem 16 Next Previous Problem List (1 point) Suppose the f(x, y) is a smooth function and th...
72 Partial Derivatives: Problem 16 Next Previous Problem List (1 point) Suppose the f(x, y) is a smooth function and that its partial derivatives have the values, f(0,-4) 5 and f,(0, -4) =-1. Given that f(0,-4) = 0, use this information to estimate the value of f(1,-3) Note this is analogous to finding the tangent line approximation to a function of one variable. In fancy terms, it is the first Taylor approximation. Estimate of (integer value) f(1,-3)
72 Partial Derivatives:...
Q5. (15pt] Consider the following system of differential equations. it t = = Ctyt - 1,...
Q5. (15pt] Consider the following system of differential equations. it t = = Ctyt - 1, c + gì - 2. (a) (3pt) Find the equilibria of this system. (b) (5pt] Draw the phase diagram of the system and analyze the stability of the equilibria. (c) (7pt] Linearize the system around (1,1) by using Taylor approximation. Find the general so- lution of this linear system of differential equations and analyze the stability of the equilibria.
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)
4. Consider the system of equations rey - ye?w = 1 +vw and usin(EU) = w sin(yw). du Using the implicit function theorem, show that (x, y) can be expressed as a differ- entiable function of (vw) near (v, w) = (0,1). Find the values of (u, w) = (0,1). Be sure to show work. and
Please solve Q 7 & 8
7. 14+6 marks] Consider the initial value problem y_y2, 2,y(1) = 1 y'= 1-t (a) Assuming y(t) is bounded on [1, 2], Show that f(t,v)--satisfies Lipschitz condition with respect to y. (b) Use second order Taylor method with h 0.2 to approximate y(1.2), then use the Runge- Kutta method: to compute an approximation of y(1.4). 8. [4 marks) Assuming that a1, o2 are non negative constants, determine the parameters o and β1 of the...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
The Implicit Function Theorem and the Marginal Rate of Substitution (4 Points) 3 An important result from multivariable calculus is the implicit function theorem which states that given a function f (x,y), the derivative of y with respect to a is given by where of/bx denotes the partial derivative of f with respect to a and af/ay denotes the partial derivative of f with respect to y. Simply stated, a partial derivative of a multivariable function is the derivative of...
1. Consider the system 2(t)--3i(t) +z2(t) +3() (a) (i) Find the linearised system at the equilibrium point (0, 0). (ii) What type of equilibrium point is (0,0)? (State your reasons fully.) (ii) Sketch the phase portrait for the linearised system near (0,0). (b) Repeat part (a) for the equilibrium point at (1,0). (c) (i) Are there any other equilibria? (ii) Read the Grobman-Hartman theorem and confirm that it applies to the above equilibria.
1. Consider the system 2(t)--3i(t) +z2(t) +3()...
5. Consider the nonlinear two dimensional Lotka-Volterra (predator-prey) system z'(t) = z(t)[2-2(t)-2y(t)l, y'(t) = y(t)12-y(t)--2(t)] (a) Find all critical points of this system, and at each determine whether or not the system is locally stable or unstable. (b) We proved in class, using the Bendixson-Dulac theorem, that this system has no periodic solution with trajectory in the first quadrant of the plane. Assuming this, use the Poincare-Bendixson theorem to prove that all trajectories (z(t),y(t)) of the system (2) with initial...
GROUP WORK 1, SECTION 14.3 Clarifying Clairaut's Theorem Consider f (x, y, z) = x?cos (y + 2). 1. Why do we know that fyyxxx=0 without doing any computation? 2. Do we also know, without doing any computation, that Sxyz = 0? Why or why not? 3. Suppose that a = 3x + ay". Jy = bxy + 2y. S,(1, 1) = 3, and has continuous mixed second partial derivatives xy and fyx. (a) Find values for a and b...
72 Partial Derivatives: Problem 16 Next Previous Problem List (1 point) Suppose the f(x, y) is a smooth function and that its partial derivatives have the values, f(0,-4) 5 and f,(0, -4) =-1. Given that f(0,-4) = 0, use this information to estimate the value of f(1,-3) Note this is analogous to finding the tangent line approximation to a function of one variable. In fancy terms, it is the first Taylor approximation. Estimate of (integer value) f(1,-3)
72 Partial Derivatives:...
Q5. (15pt] Consider the following system of differential equations. it t = = Ctyt - 1, c + gì - 2. (a) (3pt) Find the equilibria of this system. (b) (5pt] Draw the phase diagram of the system and analyze the stability of the equilibria. (c) (7pt] Linearize the system around (1,1) by using Taylor approximation. Find the general so- lution of this linear system of differential equations and analyze the stability of the equilibria.
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)
Most questions answered within 3 hours.
-
Why is the answer b), for this question? I came up with C) for
my incorrect...
asked 1 minute ago -
Suppose that you know that in the population of full-time
employees in the United States, the...
asked 23 minutes ago -
This experiment was designed originally to sample various meat and carcass quality
aspects of Ontario pigs...
asked 24 minutes ago -
Dopamine Hydrochloride: draw the structure And Show the
functional groups in different colors and label the...
asked 16 minutes ago -
A rope supports a 10 kg dumbbell hanging from it. What is the
tension in the...
asked 15 minutes ago -
) Raw materials are studied for contamination. Suppose that
the number of particles of contamination per...
asked 38 minutes ago -
After running a regression analysis we calculated an F test and
the significance level was 0.15....
asked 33 minutes ago -
----Can someone please help me solve this one using JAVA
----I thank you in advance
Create...
asked 38 minutes ago -
1. What force primarily attracts the potassium ion to
the nitrate ion?
a. London forces...
asked 40 minutes ago -
What are the negative effects of abruptly stopping the use of
all fossil fuels? Give at...
asked 47 minutes ago -
Given that many conflict are the result of different parties having
different interests, is it possible...
asked 52 minutes ago -
A 750 g block can slide uniformly along the horizontal track
when a string attached to...
asked 55 minutes ago