Left, right and the limit

You will write three small functions that test a limit by computer. The checker uses a function with a hole, a function with a jump and a plain polynomial.

The idea. A limit at $a$ looks at $f$ just to the left of $a$ and just to the right of $a$. If the two sides head for the same number, the limit exists. Take $h = 0.000001$ for "just beside".

Your tasks.

1. Finish left_value(f, a). Return f(a - h) with h = 0.000001.
2. Finish right_value(f, a). Return f(a + h) with the same h.
3. Finish limit_exists(f, a). Return True when the left and right values differ by less than 0.0001, and False otherwise.