# Search results

1. ### Taylor Expansion and Error

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...
2. ### Linearizing a system using a taylor expansion

I agree with what you're saying. That's why I didn't think the problem was as hard as it I was thinking. No function is explicitly defined.
3. ### Linearizing a system using a taylor expansion

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...
4. ### Independent Condition Probability Problem

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...
5. ### Fourier Series Help

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

7. ### Fourier Series Help

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...
8. ### Problem with a Fourier Series

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...
9. ### Work done as air expands in piston with spring

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...
10. ### Organic Chem- acid catalyzed reation

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...
11. ### Voltage dealing with two parallel plates

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...
12. ### Help Solving a differential equation

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...
13. ### MAX/MINS with multivariables

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)...
14. ### Multivariable Tangent Lines

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...
15. ### Physics Problem; help me please

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...
16. ### Integral help

I was wondering what the best way to do this integral was: Integral of 1+sin(x) all over cos(x)^2 Is subsitution the best way?
17. ### Arc Length

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...
18. ### Vector calculus

ah , i think i got it. thanks, i was being stupid
19. ### Vector calculus

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!
20. ### Another vector proof

i get that, but i don't get your last algebraic step. how did the -d1+d2 turn into d1-d2
21. ### Another vector proof

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...
22. ### Vector help

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
23. ### Vector help

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
24. ### Aqueous Equilibria Help

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?
25. ### Energy Conservation Problem

ok thanks, I got it!
26. ### Energy Conservation Problem

would that be because there is no external torques acting on the system?
27. ### Energy Conservation Problem

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...
28. ### Calculus II Problem: Dams and intergration by slicing

you also might be able to get the width of the dam by finding the arclength of the dam.
29. ### Calculus II Problem: Dams and intergration by slicing

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.
30. ### Very Important Help Series

I believe there are 86 in the terms. you take 92-7+1=86
31. ### Can some 1 do this

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...
32. ### Another Electromagnetic Induction Question

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...

no problem.
34. ### Another Electromagnetic Induction Question

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...
35. ### Question on induced emf in a loop

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:
36. ### Question on induced emf in a loop

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...
37. ### Induced emf in a loop

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...
38. ### Importance of zero

BRAVO! Palindrom! :smile: