Sriman Dutta

For a general function [math]f(x):R \rightarrow R[/math] , and if as x tends to a, there exists a discrete value l which is approached by f(x), then by definition we have: [math]\lim_{x \rightarrow a} f(x) = l[/math]. For all x in the open interval [math](a+ \delta, a- \delta) [/math], the value [math] |f(x)-l|< \epsilon [/math], for all [math]\epsilon[/math] infinitely small. If we want to make the 'tends to' part of limit as 0, then we consider h=x-a, and so, as [math]x \rightarrow a[/math], [math]h \rightarrow 0[/math]. This is a known technique of limit evaluation.

Monoatomic ions consist of single atoms for example Cl-. Polyatomic ions consist of multiple atoms. In other words, it's a radical. For example NH4+.

Thanks for the reply.

A quadratic inequality is an inequation of the form : [math] ax^2 + bx + c > 0 (< 0, >=0, <=0) [/math] The first step is to solve the quadratic equation [math]ax^2+bx+c=0[/math] and get the roots [math]r_1[/math] and [math]r_2[/math]. Then put it as: [math](x-r_1)(x-r_2) > 0[/math] Now solve it using the method of intervals. Remember that we can solve such inequalities with method of intervals only when the roots are real. Thus, discriminant should be >= 0.

Oh....that's great. I get to see it. Thanks very much. :-)

Hi everyone, Just like the Abel-Ruffini theorem limits the solution to polynomial equations upto fourth degree, is there any such check on the solutions of a differential equation? Can a complete general solution be framed for any n-th order differential equation ? Thanks in advance

GR does not consider gravity as a force. Gravity is the outcome of the curvature of space-time caused due to mass. Newton did not saw such a picture. He considered it as a purely attractive force.

Err, you're correct. That's not a good way to prove an identity. But that little example showed correct results with that.

It looks correct. Let's try a function. [math] f(x)=3x^2-a[/math] , a is a constant. [math] \lim_{x\rightarrow 0} f(x+a)= 3(0+a)^2 - a=3a^2-a=\lim_{x\rightarrow a} f(x)[/math]

Senseless talks is no science at all. If you don't believe, try it.

You can try either of the following:- oxidation number method or ion electron method.

The dot product of two orthogonal vectors is zero. A.B=|A||B|cos a, here A and B are vectors, and a is the angle between them. These are two hints to solve the problems.

Salt is more soluble in water than most other substances in the body. So the excretion of water involves removal of salts too.

For your information Roger, each and every object in the universe attracts another body. This force is directly proportional to the product of the masses of the two bodies and inversely proportional to the square of the distance between them. [math]F=G\frac{m_1m_2}{S^2}[/math] According to general relativity, any massive body creates a depression in the space-time fabric, causing any surrounding object to fall into that depression. That is the origin of this attractive force.

There is a theory regarding it. Scientists believe that many millions of years ago a large celestial body, probably a massive asteroid named Theia collided with the earth causing a huge spread of materials and rock chunks. Those materials accumulated under gravitational influence to form the moon. This theory has a major evidence to support. The nearer side of the moon, that is, the side which faces the earth, has thinner crust than the other side. According to the theory, the heat of magma from earth after the impact caused the facing side of the moon to melt, thereby delaying the process of cooling and solidification. This has resulted in a more thick crust to form on the far and cool side than on the near side.

There is no way to block gravitational field.

momentum of photons = hf/c, f is the frequency, c is the speed of light and h is Planck's constant.

Fire is an outburst of heat. It creates a shock wave of vibrating particles that causes much injury. As the shock wave is basically a spherical wave travelling at about 332 m/s, it has a lot of momentum that results in injury.

I derived the equation here: [math] KE_{total} = Work_{gravity} + Work_{upward} [/math] [math] \frac{1}{2}mv^2 = mgh. + mah cosec \theta[/math] [math] \frac{v^2}{2}=h(g+a cosec \theta)[/math] a is the acceleration of the body up the slipping surface.

Resistance of a conductor is a measure of obstruction to the path of electric current. It is mainly caused due to repulsion between moving electrons due to potential difference between the ends of the conductor and the electrons of the atoms of the conductor. The heat is generated mainly due to these collisions. [math] Q= I^2 Rt [/math] where Q is heat, I is current, R is resistance and t is time.

Example of a chemical change and a physical one will help a lot. The combustion or burning of a fuel is a chemical change. Like, burning of methane is: [math]CH_4 + 2 O_2 ---> CO_2 + 2 H_2 O [/math] On the other hand the melting of ice to water is a physical change. Clearly, a chemical change involves alterations in molecular structure but physical changes don't.

I must point out here that you may get confused between 'sqrt' and '^2' .

power = force x velocity

If initial velocity is zero, then [math]v^2=2gh = 2*9.8*450 =8820 [/math] . We are here neglecting aerodynamic drag. So, [math]K=\frac{1}{2}mv^2 = \frac{1}{2}*5*8820= 22050J[/math] And, [math] P=mgh=5*9.8*450=22050J[/math] So simple.

Hitler was aiming at world conquer. Moreover, his regime in Germany witnessed oppression on a severe scale. US could not keep quite after the Japan's bombardment of Pearl Harbour on 7th December 1941. The only course left open to US was to crush the Berlin-Rome-Tokyo Axis, of which the Nazi and Hitler were a part.