What does it mean limit X tends to zero?

For any function f(x) lim x->a f(x) The limit signifies that what will be the output of the function for the value of x slightly greater or slightly smaller than ‘a’, limit tends to 0 signifies that the value of x is not equal to zero but 0.000000000000……

How can you say that a limit exist or does not exist?

In order to say the limit exists, the function has to approach the same value regardless of which direction x comes from (We have referred to this as direction independence). Since that isn’t true for this function as x approaches 0, the limit does not exist.

When an integer is divided by 0 the result is?

When you divide by zero, the result is undefined.

What does it mean when x tends to zero?

Here x tends to zero means x is very very close to zero but not exactly zero as the function may or may not be continuous at absolute zero.

What is the limit of 1/x as x approaches zero?

The end behavior of the function will still yield a negative large number if we plug in even closer values of zero from the right, or negative infinity. As a result, the left and right limits do not equal. Therefore, the final answer is that limit of 1/x as x approaches zero is DNE (do not exist) and/or that the function diverges.

Why does 0x∞ not equal 0?

This leads to all these weird things like 0x∞ not being 0, in spite of multiplication by zero by definition being zero, since multiplication is repetition of addition. This leads to 2 things, there must 2 notions of multiplication, one defined by addition as you have demonstrated, and other as the inverse of division.

What is the value of the function when x becomes 0?

So the value of the function you get when X becomes 0 is the value the function of X is tending to, when X is tending to 0. In simple words, one can say that when X is tending to 0, the function of X tends to the value you get when you substitute 0 in the place of X