Question

Explain what happens as "x" gets farther and farther away from zero, in positive and negative direction

Answer 1

Answer:

IF X MOVES FARTHER FROM 0 IN THE POSITIVE DIRECTION, THE NUMBER WILL INCREASE

IF X MOVES FARTHER FROM 0 IN THE NEGATIVE DIRECTION, THE NUMBER WILL DECREASE

9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9

Answer 2

Answer:

When x gets farther and farther away from zero in the positive direction it increases continuously. But it can be increased forever as there is no limit and is assumed to approach a number which is always bigger than it by definition no matter how big it becomes, i.e., infinity. And vice versa for negative direction, i.e., negative infinity. Now since there is no limit till which it can increase, this is the reason its limit doesn't exist.

$\\ \lim_{n \to \pm \infty} (n) \: does \: not \: exist$