Award-Winning Calculus Tutors serving Portsmouth

The student and I continued review on volume problems, going over the disk and washer methods as well as alternative axes of revolution. We also dealt with a problem involving the cylindrical shell method. We also derived the formula for cylindrical shells using geometric intuition.

The student and I met to review for his upcoming final. We reviewed indefinite integration, bounded integrals, related rate problems, distance/velocity/acceleration problems, and Riemann sums. I am pleased to report that he was accepted into his first college, and will most likely be attending there this fall. I am very pleased with how he has progressed, and I fully expect him to succeed on his final and in college going forward. We may meet if he needs additional review time leading up to the end of the semester.

We worked on word problems involving the first and second derivative of a function. One involved a circular sunspot with a constant growth rate to its area, where both sub-questions asked for the determination of dr/dt for a specific circumstance. There was another question involving the sale of millions of gallons per year (of some liquid that I can't recall) and another that detailed the average cost for the manufacturing of CD players. Towards the end I inadvertently gave the student a preview of the integral/ antiderivative, which we will certainly focus on next week. For the second week in a row, I was told he got a ".12" on one of his homework problems, preventing a perfect score. Because he is/ was doing quite well in the class without my assistance, it's a luxury that we can spend our session time really exploring a question instead of hurrying onto the next one.

We went over a sequences and series packet. The student was struggling with some parts. She had not read the packet and I urged her to make it a habit to read the math texts that she is given and assigned. She is very bright but will fall behind if she doesn't read.

In this session the student and I began working on derivatives. We spent most of today working with the limit definition for derivatives, which has been a continuation of our previous work in large part. The algebra has gotten much trickier with this material, which is good practice for him.

I went over problems with the student involving the calculus of exponential and logarithmic functions, as well as basic definite/indefinite integration problems and area problems. Overall, he has a good understanding of how to work these problems, and I expect him to do well on his exam tomorrow.