# Tutoring Calculus, Series, Sequences, Improper Integrals and Limits

We focused on series and sequences and looked a bit at improper integrals.

All of these are connected to limits. If something diverges, which is easier to determine than convergence, you simply say it diverges. If a test is inconclusive, you try another test.

Geometric series might be the easiest to deal with. Sometimes a series doesn’t exactly look like a typical geometric series and needs to be manipulated a bit algebraically. If you have the ratio and the first term, there is a simple formula to determine the sum.

Many times for series, the variable with the highest exponent becomes more important.

An alternating series just needs to be decreasing to be convergent. To be absolutely convergent requires more tests.

The algebra before doing the calculus can be very important. Changing the look of an expression can make it easier to work with.

Knowing the trig functions is necessary for some of these problems.

U-substitution was a useful technique for some of the integration. Before calculus 3, it’s probably a good idea to review integration by parts.

e ~ 2.7

Remember the chain rule when taking the derivative of e^u (most of the time) unless taking the derivative with respect to u.

If you make a substitution in integration, you must change the bounds or label the bounds more carefully.