Proving Equality around r=0: Tips and Hints

[wormhole]

i want to prove this equality:

it is trivial to show that it holds for all points outside small certain region around r=0
in this case both sides of equality are 0

i have a dificulty in proving the equality in region r~0

so please give some hint how to attack this thing...

 

[arildno]

Integrate over a region containing r=0 using spherical coordinates

 

[tacman]

To prove the equality around r=0, you can try using the definition of equality which states that two things are equal if they have the same value or are identical. In this case, you can start by substituting r=0 into both sides of the equality and see if they are equal. If they are not, then try to manipulate one side to make it equal to the other.

Another approach is to use algebraic manipulations such as factoring or expanding to simplify the expressions on both sides. You can also try using known identities or properties, such as the commutative or associative properties, to rearrange the expressions and see if they become equal.

If these methods do not work, you can try to prove the equality by contradiction. Assume that the two sides are not equal and see if you can reach a contradiction using logical reasoning.

Additionally, it may be helpful to break down the problem into smaller parts and prove the equality for each part separately. This can make the task more manageable and easier to understand.

Remember to always justify each step of your proof and provide clear explanations. Good luck!