Problem 2 Find max, min, point of infliction for
a. f(t)=c (e^(-bt)-e^at ) for t≥0 where a>b>0, c>0
b. f(x)=2x^3+3x^2-12x-7 for -3≤x≤2
c. f(x)=(x+3)/(x^2+7) for -∞≤x≤+∞
u(t−c) =uc(t) ={0, 0≤t<c,1, t≥c.}
USE Laplace Transform to solve
y′′+ 2y′+ 2y=δ(t−5)e^tcost, y(0) = 1, y′(0) = 2, whereδ(t)is the
Dirac delta. Does the solution show a
resonance?
A particle is moving according to the given data
v(t)=t^2 - sqrt(t), x(0) = 0, 0 ≤ t ≤ 4.
• Find x(t), the position of the particle at time t.
• For what values of t is the particle moving to the left? To the
right?
• Find the displacement of the particle.
• Find the total distance covered by the particle.
Given the two lines
(x, y, z) = (4, -3, 5) + t(2, 0, -3)
(x, y, z) = (4, -3, 5) + s(5, 1, -1)
a) determine a vector equation for the plane that combines the
two lines
b) parametric equations of the plane that contains the two
lines
c) Cartesian equation of the plane that contains the two
lines
t^2 y'' − 4ty' + 6y = t^4*e^t , t > 0. Use variation of
parameters to find a particular solution given that y1 = t^2 and y2
= t^3 are a fundamental set of solutions to the corresponding
homogeneous equation
(1)
(2)
(3)
DI
C
DI
C
DI
C
$0
$4
$0
$65
$0
$2
10
11
80
125
20
20
20
18
160
185
40
38
30
25
240
245
60
56
40
32
320
305
80
74
50
39
400
365
100
92
Refer to the given consumption schedules. DI signifies
disposable income and C represents consumption
expenditures. All figures are in billions of dollars. At an income
level of $40 billion, the average propensity to consume
is...
The temperature at a point (x,y,z) is given by
T(x,y,z)=200e^(-x^2-y^2/4-z^2/9) , where T is measured in degrees
Celsius and x,y, and z in meters. just try to keep track of what
needs to be a unit vector. a) Find the rate of change of the
temperature at the point (1, 1, -1) in the direction toward the
point (-5, -4, -3). b) In which direction (unit vector) does the
temperature increase the fastest at (1, 1, -1)? c) What is...