Question

lim (-1/x) = infinity
(x->0-)
as the limit of x approaches 0 from the left, how do you know that -1/x = infinity? When sketching the graph, I can understand it, but I want to know the reason so it'll help me understand in future problems.


thanks!

Answer 1

is it because t is getting infinitely smaller without being able to reach 0 because 1/0 doesn't exist?

so if the limit were approaching 0, it would not exist
if the limit were approaching 0 from the right (assuming it was 1/x) it would be positive infinity as well?

Answer 2

From the left you should have -infinity. What you end up with is, a number like 1 divided by 10,000,000. Substituting, a large number for x.

Answer 3

From the left you should have -infinity. What you end up with is, a number like -1 divided by 10,000,000. Substituting, a very small number less than 0.

Answer 4

Make a table of values, it might help you see it.

Answer 5

1/-0.01 = -100
1/-0.0001 = -10000
1/-0.00000001 = -100000000

Answer 6

\(x \to 0^-\)
what does that tell you about 'x' ??
positive or negative ?

Answer 7

and this might be quite obvious to you,
positive number / 0 = +infinity
negative number /0 = - infinity