Question

How do you find the limit of `2x-1` as `x->0`?

Answer 1

See below.

Explanation:

If `x` is very, very close to `0`, then `2x` is close to "`2" times " 0`", which is `0`.

And `2x-1` or "`2x" minus "1`", which is close to `0-1` which is `-1`.

So,

`lim_(xrarr0) (2x-1) = -1`.

Note 1: We don't usually write out the reasoning I presented.

Note 2: The function `f(x) = 2x-1` is well-behaved in the sense that we can find the limit at any value of `x` by plugging in the number (by substitution).

We call functions that are well behaved in this way "continuous" functions.