eli5: what are limits in calculus???

Question

eli5: what are limits in calculus???

In: Mathematics

Answer 1

Sometimes you have an expression that’s undefined for some value of x. For instance…

(x^2 – 5x + 6) / (x-2)

…doesn’t work if x is 2. You get a division by zero which we can’t handle. Limits give us a way to analyze stuff like that – basically we say, “ok, 2 doesn’t work, but what if x were 2.1, or 2.001, or 2.000001”.

We can actually do one better than that, and figure out how the function would behave at (2 + 1/infinity), i.e. infinitely close to 2, and the value there is called the limit.

(For the thing above, the limit should be -1. You can sort of see that if you plug in x=2.001, or x=1.999, to see how it behaves close to 2.)