Award-Winning Calculus Tutors in Cambridge

The student and I continued finding limits algebraically today. The student has shown tremendous improvement in finding limits, whether normally, by simplifying expressions to avoid indeterminate forms, by piece wise functions, or though infinite limits.

Today we started an introduction to limits. We went over how to find holes, horizontal asymptotes, and vertical asymptotes and their relationship to limits. Finally we discussed using limits as values in equations as well as how to find specific limits in given functions.

The student and I went over some examples of real world applications of Linear Optimization. We used examples from a quiz his teacher gave him, and once he solved those I gave him a few other examples to work on. I then had him teach me what he had learned in order to further re-enforce the learning

The student had another calculus test coming this Wednesday and wanted to review for it. So we did review problems that covered the following: 1. Taking derivative of logarithm functions. 2. Finding the limit using L'Hopital's rule or using natural logs. 3. Taking the integral of exponential/logarithm functions. She also mentioned at she did get an A- on her last test and I was happy to hear that!

Today we worked on test prep for midterm 1. We quickly discussed each section (1.1-3.4) on the exam and determined where further review was needed. Then we focused on material for 3.3 and 3.4, discussing the idea of the derivative as the slope of the tangent line and the mechanics of determining the derivative as the limit of the difference quotient. We are working to improve the student's algebra skills in conjunction with the calculus concepts, and I gave some pointers on successful test taking (organizing work, showing key concepts and checking answers). I asked him to go through the material in his text and make his own notes before the test.

In this lesson, we went over the Fundamental theorem of calculus and applied it to a variety of problems. We looked at how it applies to areas under the curve, as well as word problems involving the antiderivative of some rate of change function. Then we moved on to integrating by substitution. We did a lot of practice with it and, by the end, she was really getting the hang of it.