• This web page describes an activity within the Department of Mathematics at Ohio University, but is not an official university web page.
• If you have difficulty accessing these materials due to visual impairment, please email me at mohlenka@ohio.edu; an alternative format may be available.

main calculus sage page

Limits

We can try to guess a limit by trying numbers close to our target point.

You can take limits. Try sin(1/x) at x=0 to see what happens.

You can (graphically) test against the definition of a limit. The default delta is too large, so the function goes outside the interval [L-epsilon,L+epsilon]; make delta smaller until it makes the function stay in the interval. Then make epsilon smaller and then find a sufficiently small delta for that epsilon. Repeat. What would happen if we had the wrong L?

You can take limits from the left or right.

You can define a function and take limits involving it. We had to declare that h was a variable, otherwise it would be undefined and give an error; only x is assumed to be a variable.

You can illustrate the Squeeze Theorem.

You can take limits at infinity. Try it for sin(x).

You can evaluate limits that are infinite.