Award-Winning Calculus Tutors serving Chesterfield

In our session, we continued to work on the review worksheet that the student's TA gave him. However, we started by first having him tell me what they had covered in class since we last met and whether it was making sense to him. He told me that they had further discussed limits and began to learn about the product and quotient rules. He seemed to have some difficulty remembering the rules themselves, so I gave him a few mnemonic devices that helped me. The problems that we did in the worksheet revolved mostly around taking the first derivative using the power rule, which he has a pretty strong grasp of.

We started this session by covering the graphs of functions as they relate to the graphs of their derivatives. This was a difficult topic to which we will return in the future. We then turned our focus to finding the derivative of a function based on the limit definition of a derivative. We concluded by identifying horizontal and vertical asymptotes of functions. We will be meeting frequently over the next couple of days in order to ensure that the student is prepared for his midterm. For extra practice, I gave him an activity where he had to match the graphs of functions to the graphs of their derivatives. I also asked him to work through another example using the definition of a derivative.

The student reported that she got a 23 on her last test. She had the test and we went through each problem and worked through what she did wrong. Several mistakes were caused by dropping the sign of a number or manipulating the equation when she didn't have to. We continued to work on homework problems that she had difficulty with. I think this session helped her get more confident about working these types of problems.

The student and I spent the session reviewing for her upcoming Calculus test. We first completed homework problems on new material, which covered taking the integrals of functions and then graphing it. We then worked on a review for her test that was given in class. She did well on solving the problems in the review. We also reviewed the difference between an indefinite and a definite integral, and practiced finding the definite integral.

The student continued reviewing the first derivative test for relative extrema on a closed interval; we also used the second derivative to find relative extrema, points of inflections and concavity. We used the power, product rule and chain rule. We also began reviewing exponential and logarithmic functions and their properties.

Today we covered the basic methods of approximating definite integrals: left hand sum, right hand sum, trapezoid rule. The student did two illustrative problems during the session.