Answered: B. Use Green's theorem to evaluate f… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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B. Use Green's theorem to evaluate f (x²y)dx + y²dy
Where C is close path formed y = x and y = x³ from (0,0) to (1,1).
Q5: Consider the CT signals to Compute y(t) = h(t) * x(t).
h(t)
2
x(t)
ET
1
NOTE { convelution operator}
t

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Let x=x(t) be a twice-differentiable function and consider the second order differential equation x+ax+bx=0(11) Show that the change of variables y = x' and z = x allows Equation (11) to be written as a system of two linear differential equations in y and z. Show that the characteristic equation of the system in part (a) is 2+a+b=0.
(a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t. Then (b) evaluate dw/ dt at the given value of t. 1. w = x2 + y2, x = cos t + sin t, y = cos t - sin t; t=0 2. w = x/ z + y /z , x = cos^2 t, y = sin2 t, z = 1/t ; t =3
(a) express dw/ dt as a function of t, both by usingthe Chain Rule and by expressing w in terms of t and differentiatingdirectly with respect to t. Then (b) evaluate dw/ dt at the given valueof t. w = z - sin xy, x = t, y = ln t, z = et-1 ; t = 1
Suppose at (0,1) the function f(x,y) has linearization L = 2x + 3y -3. Let v = <1,0>. What are f(0,1) and Dvf(0,1)?
Determine two functions, defined on the interval ( − ∞ , ∞ ) , whose Wronskian is given by W ( f 1 , f 2 ) = e 2 x . Are the functions that you found linearly independent on ( − ∞ , ∞ ) ? How do you know?
Compute the discriminant D(x, y) of ƒ(x, y) = x2y2.

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