Recent Tutoring Session Reviews
"Today, we continued our work on derivatives of polynomials. I introduced the student to the product rule, the quotient rule and the chain rule. He picked up on the rules very quickly, only struggling a little with the chain rule which is a complicated concept. We spent the session going over these rules and working through examples and practice problems to make sure he understood them. I'm very impressed with how quickly we are moving through the material and how quickly he is picking it up."
"The student and I reviewed material from our previous meeting, spending most of our time working on finding areas under curves and more complex implicit differentiation. He has improved much with practice, and the more complex problems revealed his weak points (such as derivatives of terms with variable exponents) and allowed us to improve upon them. Overall I think this strengthened his understanding of the material we have covered thus far, and he will most likely be ready to move on to new material for our next session."
"Today we covered in depth series and sequences. This lesson started out with the basics: a review of geometric series and partial sums, but quickly added new tests for convergence. We covered the divergence theorem, telescoping series, the geometric theorem, alternating series test, root & ratio tests, direct and limit comparisons, improper integral test, and p-series test. He seemed to have a good grasp of what each test did. I suggested some more practice on his own with those, but there is no rush. This was a great penultimate session!"
"Today we continued with the u-substitution integrals. The student understands where and why to use u substitution, and can execute u substitution both for the function of u, and for du. We have gone over the geometric representation of a u substitution, and have jumped ahead and talked about the geometric representation of an integral as an area, which helped with the understanding of the u-substitution process."
"We went through finding the formulas for taking derivatives of the inverse trigonometric functions as well as several problems for both the inverse trigonometric functions and logarithms. The student is doing well using all the rules up the chain rule and taking derivatives of the natural logarithm functions and she is doing better with the rest of the inverse functions. I left her a worksheet that has a variety of functions to take derivatives of that covers all the rules aside from implicit differentiation. We also started looking at using derivatives to analyze a graph from its function by finding local/ absolute maximums and minimums and critical points. We hope to at least get through curve sketching during our last session next week."
"We practiced LRAM, RRAM, and MRAM area methods to solve for areas under curves. Went over u substitution and talked about concerns for upcoming final exam. I suggested that the student should read up on business related calculus concepts instead of trying to memorize equations."