One-sided limits by computer

You will write three small functions that estimate the left-hand and right-hand limits of a function at a point, and test continuity. The checker uses a hole, a jump and a smooth function.

The idea. The left-hand limit is the value of $f$ just below $a$, and the right-hand limit is the value just above $a$. For a tiny number $h$, the numbers $f(a - h)$ and $f(a + h)$ estimate them. A function is continuous at $a$ when both estimates agree with each other and with the value.

Your tasks.

1. Finish left_limit(f, a). Return f(a - h) for h = 0.0000001.
2. Finish right_limit(f, a). Return f(a + h) for the same h.
3. Finish is_continuous(f, a, value). Return True when both limits are within 0.001 of value, and False otherwise.