Question

In limts, we speak of the value of a function when it tends to a given number. As we say:

lim_x-->a f(x), we mean to say we are trying to find the value of f(x) as x tends to a number a.

But how close exactly is this? I mean how close to a should x be when we say x-->a. The value of x can be a + 0.0001 or it can be a + 0.000000001. So what should the value of x be as we say x tends to a?

Answer 1

its infinitesimely close to the value .

Really tends to implies most close number. as the numbers are infinite in nmuber , we cant give an exact value for the tends to.

so it can take much smaller value than what you written.
just make a sense that , it is to tell x->a means it is getting close to a but not equal to a
so i think you got the idea.
LIKe if satisifed