Recent Tutoring Session Reviews
"Today we started going over exercises the student worked on at home, having to do with slopes, limits, domains and graphing. We reviewed how to find the domain, and the different between the x-values in the domain and evaluating a limit. We will have to work on domain a little more, but he has grasped the concept well. We solidified his understanding of vertical and horizontal asymptotes graphically and algebraically. We went over the point-slope versus standard form of a line equation. We also discussed how to find the equation of a line tangent to a point using the first derivative. We defined what a derivative is and when a derivative can be defined at a point, and compared taking a derivative to finding "m" with the simple line equation. We did a problem on continuity, confirming the student's understanding of it. He took the derivative of many complex functions, working on using the power, chain, quotient and product rules when necessary. We started discussing how to find critical numbers, max, min and inflection points using the first and second derivative test. This week we will continue to focus on application of derivatives in such ways, as well as in the context of related rates and optimization. We will also start taking the integral of functions and applying this concept to word problems."
"Today's session was our last chance to meet before the student's final exam the next day, so we planned on a long session to cover everything. We began by finishing his final exam review sheet, which picked up right back at finding critical points through derivation. This allowed us to continue practicing combinations of the chain and product rule and discussed utilizing the chain rule in logarithmic and sinusoidal functions. As his class is a business calculus course, we worked on writing a function for price and revenue given a real scenario, and how to go about maximizing these functions. Our discussion moved into more conceptual material, as he felt he understood the procedures well but lacked the meaning and purpose behind what we were doing. We related derivatives and critical point values to the shapes of functions, and examined limits in a qualitative way. He felt much more comfortable after our discussion of limits, as this concept was very abstract and unusual to him, and connected limits to evaluating improper integrals. We also continued practicing a lot of problems with u-substitution, focusing on how to identify what to choose for our u. He shows that he knows the material."
"The student's final is tomorrow, so we did practice and went over more of his past exams. His knowledge of the chain rule and product rule has come a long way. He's also solid in his ability to determine continuity. He has worked hard all semester, and I think he's prepared to do well on the exam."
"The student and I went through graphing functions and finding their max and/or min, critical points in general, endpoints, asymptotes, and end behavior regarding limits. We also practiced finding the limits for problems involving indeterminate forms by using L'Hopital's Rule."
"Reviewed/reworked most recent test, began Riemann sums and integrals. Next session: completing 5.2 and 5.3 online homework."
"We continued to look at vectors, lines, and planes in 3D space. I demonstrated various concepts related to how lines and planes can be arranged in space, using illustrations and models (pens and sheets of paper). We looked at various examples in the book on how to solve different types of problems, using cross products, etc."