Mathematics Limit Question please help?

x -> ∞

That's math talk for x gets bigger and bigger beyond all imagination well past the millions and trillions.

e^x so how does this behave while x is getting bigger and bigger? If you not sure just plug some numbers into your calculator and you soon see its getting bigger also. (As it happens it gets bigger faster and better than x but all that really matters is we can say e^x-> ∞

adding 5 to an enormous number doesn't make a practical difference its still enormous. We still have a number that's well past all imagines. In fact at this point adding/subtracting 1000000 or any number you can write down won't effect the issue.

So next we have 1 divided by this enormous number. If you not sure you check out what happens to 1/y as y gets bigger. (I only write y there to stand for 'a number' and don't want to get mixed up with the x that's already in the question.) If you not sure look at 1/10: 1/100: 1/1000 etc up into the millions or think about about dividing one loaf divided between millions of people and how much bread do they each get? I think we can see that the fraction 1 over a great big number is tiny in fact as the bottom of the fraction becomes unbelievably big then the value of the fraction is so small you have to break atoms to give people their fair share. We say -> 0.