Homework Statement
For g=Hf = sin (f), use a Taylor expansion to determine the range of input for which the operator is approximately linear within 10 %
Homework Equations
The taylor series from 0 to 1 , the linearization, is the most appropriate equation
The Attempt at a Solution...
Homework Statement
Linearize the system operator illustrated below by applying a Taylor series expansion.
f(t) ----> e^f(t) -----> g(t)
Homework Equations
I only find the general form of a taylor series relevant.
g(x)= sum (0,infinity) of [f^n*(a)*(x-a)^n]/n!
The system is...
Hello, I had this problem to do for statistics. I am pretty sure I did the first two parts correct. The third, I am not so sure about. I'd appreciate and guidance.
A player of a video game is confronted with a series of four opponents and an 80% probability of defeating each opponent. Assume...
My new basis of thought is that the a(n) Fourier coefficient can only be positive 6/npi... is this correct... if figure when you add the negative term, the coefficient becomes zero again. At no point can it be negative.
Correct me if I am wrong.
Thanks
Can anyone help me out with this?
Find the steady state periodic solution of the following differential equation.
x''+10x= F(t), where F(t) is the even function of period 4 such that
F(t)=3 if 0<t<1 , F(t)=-3 if 1<t<2.
Im basically just having a problem findind the general Fourier...
Can anyone help me out with this?
Find the steady state periodic solution of the following differential equation.
x''+10x= F(t), where F(t) is the even function of period 4 such that
F(t)=3 if 0<t<1 , F(t)=-3 if 1<t<2.
Im basically just having a problem findind the general Fourier...
There's a problem in my thermo class that I think I have the right answer for, but the value I get doesn't seem to make sense. The problem reads:
Warm air is contained in a piston-cyliner assembly oriented horizontally. The air cools slowly from an intial volume of .003 m^3 to a final volume...
Hey can anyone help me with this question?
What is the major product from the acid-catalyzed hydration of 3-methyl-2-pentene?
a. 3-methylpentane
b. 3-methyl-1-pentanol
c. 3-methyl-2-pentanol
d. 3-methyl-3-pentanol
e. 3-methoxypentane
Would the answer by D? My reasoning is that when...
Hey guys. I'm having trouble analyzing a part of this problem.
Two conducting, infinite sheets of charge (with thickness a) are fixed perpendicular to the x-axis as shown. The sheet from x = -2a cm to x = -a has a net charge per unit area -s and the sheet from x = +a to x = +2a has a net...
Hello, i was wondering if someone can help me along with solving this differential equation.
(x+2y)y'=y
I believe you use substitution. Right now I am setting my substitution to
v=(x+2y), but then when i follow through with my work, it doesn't simplify down to a seperable or first order...
Hey I was wondering if anyone can tell me if i am doing this right.
f(x,y) = xy^2 ; R is the circular disk x^2+y^2<=3
So first i took the gradient, since I know a mix/min can exist if the gradient is equal to 0.
Gradient of X= y^s
Gradient of Y= 2xy
So the point (0,0)...
Hello, I was wondering if anyone can help me with this problem.
Show that the line with equation 2ax+2by=a^2+b^2
is tangent to the circle with equation 4x^2+4y^2=a^2+b^2
If this is true, wouldn't the derivative of the circle equation be equal to the first equation? Would I just take...
Well, you have a fairly basic question that comes from Netwon's second law of motion. By constant pull, the system has a constant force that is pulling the train along. This means that the system also has constant acceleration, which is given by Netwon's Laws.
F = M A
You can easily find...
Hello, I was wondering if someone could check and see that i did this problem right. You need to find the arc length of the vector from t=0 to 1:
r= <2e^t,e^-t,2t>
So first i took the derivative and got velocity.
v=<2e^t,-e^-t,2>
Next i used the formula for arc length.
arc...
Hello, I just learned how to do these types of problems, but I'm having trouble. Can some one direct me through this problem?
Find the point or points on the curve which the curvature is a maximum for
a. y=ex
b. xy=1
any help is greatly appreciated. I really am stuck here!
hey guys, i am stuck on one more problem. Can anyone guide me onto the right path on how to start this?
Use this formula for the perpendicular distance between a point and a plane
D= |ax+by+cz-d| all over the square root of (a^2+b^2+c^2)
to show that the perpendicular...
Hello, can anyone guide me with this problem?
Find nonzero vectors a ,b , and c such that a x b = a x c but b does not equal c
I would appreciate any help. Thanks
Hello, can anyone help me with this problem?
Find an equation of the plane through P (3,3,1) that is perpendicular to the planes x +y = 2z and 2x +z =10
Thanks
I am stuck on this question...can anyone help?
What is the pH after .10 mol NaCN is added to 100 mL of .050 M of HCN?
(Ka=6.0x10^-19)
I think I have to use the Henderson-Hasselbalch Equation. Is this the right way to take. And if so, how should I go about getting the ion concentration?
Hey, I was wondering if anyone can help analyze this problem with me. Here is the question.
A swing seat of mass M is connected to a fixed point P by a massless cord of length L. A child also of mass M sits on the seat and begins to sing with zero velocity at a position of which the cord...
i would find the volume of the damn using D=\frac{M}{V}
I'm not sure on that. Once you get volume,
do volume times density to get mass. Multiply mass by 9.8 m/s^2. I think that's it, but could be wrong.
It's really not necessary to use Simpson's Rule. Find an volume by cross-section. In order to do that, you need to develop an equation for the area, in this case a square. By the equations you gave, the length of one side of the square would be 4-[(x^2)-2]. Since the cross-sections are...
I think I made a little progress. After drawing a force diagram, I think I could say that the magnetic force = the x component of the force of gravity(i split gravity into components rather than anything else). so then i said that:
mg\sin{\theta}= \frac{B^2L^2v}{R}
and then solved for v...
Again, this is a problem I got in my AP Physics Class can anyone help? I would really appreciate any help. My teacher didn't explain this concept too well.
A metal bar with length L, mass m, and resistance R is placed on frictionless, metal rails that are inclined at an angle \theta...
Its ok, I found out how to do it. I forgot to mention that the Magnetic field has an initial magnitude of .750 T, and is decreasing at a rate of -.0350 T/S (there's your reason for changing magnetic flux) :approve:
Hey, I'm in a high school AP class and am stuck! Can anyone help me with this problem concerning induced emf? I would surely appreciate it.
There is a loop of wire, shaped like a square. Each side is 20 cm long.
There is a magnetic field directed into the page.
What would be the way of...
Hey, I'm in a high school AP class and am stuck! Can anyone help me with this problem concerning induced emf? I would surely appreciate it.
There is a loop of wire, shaped like a square. Each side is 20 cm long.
There is a magnetic field directed into the page.
What would be the way of...
Hmm
Technically speaking, isn't that formula just for 1st order reactions. When you start dealing with zero order and second order reactions, concentrations are involved and make a difference.
Continued
Its only more practical to treat zero more like a number. Do we ever say "I have infinity apples?" It makes sense to say that I have zero apples. Plus, we use infinity usually to see how something behaves (something like a series) as it approaches infinity. We even do the same thing...
Agreed
I agree. Just accept the number. What did it ever do to you? In any system, like one with mathematical relations has to define what "something" is, on the contrary, it must also define what "nothing" is. Don't major in philosophy.