The solutions to Quiz #3 are available from the Test & Quiz Solutions link at the top of the page.

Thursday in Calc I, we answered lots of homework questions on limits. We then took a brief look at limits involving the trigonometric functions. The good news was that all of these functions, as long as we stay away from any "bad" x-values, work with our "plug-in" method for limits. We learned about two special limits involving the sine and cosine functions as we approach x = 0. Then we took the quiz.

Tomorrow, we'll talk about exponential and logarithmic functions with regard to limits. We'll see you then.

Quiz #3 happens Thursday, September 11th. It will consist of precisely one problem involving the formal definition of a limit. The rest will consist of evaluating some limits using the shortcuts, and limits involving infinity.

Wednesday in Calc I, we fully explored limits involving infinity. First up was the concept of a limit at infinity. If "the limit of f (x) exists as x goes to infinity equals L", this means that we can make the value of f (x) as close to L as we like by taking x sufficiently large. (A similar definition exists for "the limit of f (x) exists as x goes to negative infinity equals L," with the change being that we end with "... taking x sufficiently large negative.") We saw that any line y = L for which L was such a limit was a horizontal asymptote.

We looked at examples involving algebraic functions, using the trick of dividing all terms in our function by the highest power of x in the denominator of the function as well as the fact that the limit of 1/x ^r = 0 for any positive r as well as for any negative r for which x ^r exists.

We then examined function limits whose values are infinity or negative infinity. Visually, the associated x-values correspond to vertical asymptotes on the graph of the function.

On Thursday, we'll talk about limits involving trigonometric functions and start dealing with limits of exponential and logarithm functions. Plus we'll take the third quiz.

We'll see you then.

Today we answered a lot of homework regarding the delta-epsilon proofs for limits, as well as some regarding how to work with limits of functions involving the indeterminate 0/0 (factor, or expand, followed by cancelling).

We looked at the Squeeze Theorem (sometimes called the Sandwich Theorem, or Pinching Theorem) as a way of getting limits when the "product rule" for limits won't work. We then introduced the idea of infinite limits and limits at infinity.

We'll continue the discussion on Wednesday.

The solutions to Quiz #2 have been posted on the Test and Quiz Solutions page. (You'll get the quizzes back on Wednesday...)

This will be a short entry due to pressing time constraints!

Today we talked as briefly as possible about the formal definition of a limit. (Deltas and epsilons ...) We went over the proof of why the limit as x approaches 3 of 4x - 5 equals 7, and how the deltas and epsilons quantified the idea of "closeness." Then we took the second quiz.

On Monday, we'll finally get to those shortcuts on limits. See you then.