[bluescreenofdebt]

Question 3:
The magnet will become demagnetized eventually. The energy comes from the alignment of the magnetic domains being slowly destroyed (which actually means that you get equal amounts of particles in domains pointing in all directions as time goes on).

Question 4:
Have to keep in mind that our perception of these events takes a certain amount of time to process. As far as our body is concerned the events take place at the same time since we can't process fast enough to tell there's any time difference between those two events (sound travels fairly quickly, not to mention light). Any difference you see is purely your perception playing tricks on you.

Question 5:
d/dx(x^x)=d/dx(exp(ln(x^x)))=d/dx(exp(x lnx))=exp(x lnx)*(lnx+1)=(lnx+1)*x^x

Am I allowed to pose a question? This is one of my favorites:
x=y
x^2=yx
x^2-y^2=yx-y^2
(x-y)(x+y)=y(x-y)
x+y=y
but remember x=y
x+x=x
2x=x
2=1

[ARPAN]

i am extremely sorry for my mistake.
the second function is x+x+x+x+....... x times

now what do u say

[ARPAN]

for the question posted by bluescreenofdebt.

steps where the question fails to obey mathematical principles

that basically is a mathematical illusion. the fault lies in the third step where u get 0=0
(considering the fact that x=y)
and then moving over to the fourth step (which equates 0*x= 0*y=0) which is baseless here since zero multiplied by any finite number gives zero and equality that x=y need not hold.
further the step x+y=y can be reduced to x=0 i.e. what i have been saying has been proved mathematically...i.e. x=y=0

ultimately what u get is that in the entire steps u have been equating 0=0

CONVINCED!!!

[ARPAN]

i am extremely delighted to receive questions from members.
do post any queries and doubts
suggestions on any topic are also welcome

[neutralino]

Originally Posted by bluescreenofdebt Am I allowed to pose a question? This is one of my favorites: x=y x^2=yx x^2-y^2=yx-y^2 (x-y)(x+y)=y(x-y)

On going from here to the line below you divide by zero. This is not allowed.

x+y=y but remember x=y x+x=x 2x=x 2=1

Originally Posted by ARPAN i am extremely sorry for my mistake. the second function is x+x+x+x+....... x times now what do u say

Your problem here is saying that the derivative of x+x+x+...+x (x times) is equal to 1+1+...+1 (x times). This isn't true, since the part (x times) is a function of x, and thus you can't just differentiate the function term by term, but need to use the product rule.

[ARPAN]

neutralino, i am not entirely convinced with ur answer although u r partially correct, i would like u to get through a good calculus course because u reasoned that use of product rule must be done without mentioning why
secondly i wanted to know whats wrong in the second approach rather than suggest an alternative approach..

question 5.

N blocks are placed on a horizontal surface and connected to each other by means of inextensible ropes. a force F is applied on the first block causing the entire system of blocks to move. find the tension in the rope connecting Pth and (P+1) th blocks

a. when the surface is smooth
b. when coefficient of friction between surface and block is k

assume mass of first, second ..Nth blocks as m1, m2,....mN

[ARPAN]

Foucault’s pendulum
Earlier, I spoke as if a frame of reference attached to the surface of the
rotating earth was just as good as any other frame of reference. Now,
with the more exact formulation of the principle of inertia, we can see
that that isn’t quite true. A point on the earth’s surface moves in a circle,
whereas the principle of inertia refers only to motion in a straight line.
However, the curve of the motion is so gentle that under ordinary condi-
tions we don’t notice that the local dirt’s frame of reference isn’t quite in-
ertial. The first demonstration of the noninertial nature of the earth-fixed
́
frame of reference was by Leon Foucault using a very massive pendu-
lum (figure n) whose oscillations would persist for many hours without
becoming imperceptible. Although Foucault did his demonstration in
Paris, it’s easier to imagine what would happen at the north pole: the
pendulum would keep swinging in the same plane, but the earth would
spin underneath it once every 24 hours. To someone standing in the
snow, it would appear that the pendulum’s plane of motion was twisting.
The effect at latitudes less than 90 degrees turns out to be slower, but
otherwise similar. The Foucault pendulum was the first definitive experi-
mental proof that the earth really did spin on its axis, although scientists
had been convinced of its rotation for a century based on more indirect
evidence about the structure of the solar system.


which is then correct i.e. does earth rotate about its own axis and if it does then what is wrong with Foucault’s pendulum

[neutralino]

Ok, let's take a look at what you want to do. You have said that you want to differentiate the function f(x)=x^2=x+x+x+...+x (with x terms), and you say that the answer is f'(x)=1+1+1+...+1 (with x terms). But this answer contains an x (namely in the part "x terms") which you haven't differentiated with respect to! This, there arises a second term x+x+x+...+x (with 1 term). Summing the two gives 2x, which is the answer.

secondly i wanted to know whats wrong in the second approach rather than suggest an alternative approach..

I've just told you what is wrong above!![/size]

[ARPAN]

neutralino, i am extremely sorry if i have hurt u , but all i expected was a clear and distinct answer from u

i appreciate ur answer and at the same time present mine.

undoubtedly both the forms represent the same expression i.e. x^2
while the first answer can be derived from the first principles of diffrentiation

the second one fails because we assume x as a constant in one case and variable in other case as shown by neutralino which proves the fallacy of the second answer.

pls keep trying other questions

[neutralino]

Originally Posted by ARPAN neutralino, i am extremely sorry if i have hurt u , but all i expected was a clear and distinct answer from u

Don't worry, things like that don't hurt me; I was merely pointing out that you shouldn't assume things about someone.

Still, I don't really see what the point of this thread is. Either you are asking questions that you don't know the answer to and are confused with, or you are posting questions to try and test people. Either way, my first solution was probably sufficient, especially if the latter is true. So.. are you trying to test me, or are you seeking knowledge?