Limit Table: Watch a Formula's Values as the Input Closes In, From Both Sides or Toward Infinity

Opens on Chapter 7’s example: (x² − 9) ÷ (x − 3) as x closes in on 3.

Formula one letter, numbers, + − × ÷ ^ ( ), ² ³, e, π, √, ln

As the input closes in on a number, or ∞

Steps (or, for ∞, the inputs) separate with commas

Load another example from the book

Enter your numbers, then press Work it out.

How it works

Close in from both sides with smaller and smaller steps and read the values. If both sides settle on the same number, that's the limit. A formula like (x² − 9) ÷ (x − 3) gives 0 ÷ 0 at 3 itself, which isn't an answer; but its values near 3 settle on 6, because for every x except 3 it equals x + 3. Toward infinity, try bigger and bigger inputs. If the two sides settle on different numbers (a jump), there is no limit there.

From the book, Chapter 7. Closing in on 3: 5.9, 5.99 from below and 6.1, 6.01 from above: the limit is 6. Cost per print: $60.40 for 10 prints, $1.00 for 1,000, $0.4006 for a million, heading for $0.40. (1 + 1/n)ⁿ: 2, 2.613, 2.7146, heading for e = 2.71828… Every chapter and its calculator →

Numbers can be typed as 1,450, $38, 0.40, 12%, 1/6 or 2 3/8. Functions can be typed as 16t², 6 + 48t − 16t^2, 1000e^(0.05t) or √x; answers are rounded half up, the way the book rounds. Everything stays in your browser: no sign-up, nothing stored or sent.