Recent Tutoring Session Reviews
"We went over the MVT and L'Hopital's rule today. Once I explained the concepts to him with examples, he had no problem understanding them. There was a lot of homework which we hadn't touched, but he said since a lot of it was just computation, he could take care of it himself."
"We studied techniques and applications of differentiation. We did problems using the product rule, quotient rule and chain rule to find the derivatives of functions and then find the slope and equation of the tangent line to the original functions at a given x value."
"We spent a good portion of today covering topics in algebra: exponents, factoring, and multiplication by a common denominator. Some of it went very well; some was a struggle. In particular, the techniques of distribution and multiplying by a common denominator proved to be tricky. If you have any extra time, I recommend practicing these concepts and more. Algebra is a useful skill to know, and although we don't cover it explicitly in calculus, I'm hoping that you'll naturally grow more comfortable with some algebra techniques. We also introduced the first rule of differentiation. Memorizing about nine of these rules will give us a useful shortcut method for calculating derivatives functions. For homework, see the email I sent you. The derivative problems are the main focus for next session. The next 2-3 sessions will involve less theory/concepts and lots of practice. I'd also like to spend a few minutes talking about some calculus terminology/ notation in our next session."
"We covered specific questions on integration, and disk/ washer/ shell method of integrating 3d structures. The student struggled the most with concepts not taught in calculus, but pre-calculus. The student had a neutral-positive attitude towards the material."
"Today we reviewed everything the student and I have gone over in the past few months. She remembers well and performs excellently with derivative problems and their applications, including finding the critical numbers of functions. She needed a review of limits, a more esoteric part of mathematics, and I obliged her. I went over all the techniques I know of for evaluating limits, including direct substitution, factoring and dividing out, L'Hopital's Rule, small angle sine approximation, and just plugging in numbers successively closer to the limit."
"We reviewed what we covered last week, and then we looked at derivatives a little bit more in depth. We worked on comparing graphs of functions to graphs of their derivatives to try to get an intuitive understanding of what a derivative is. Most students can learn the formulas for taking derivatives, but it's crucial to be able to intuitively understand what the graph of a derivative represents, and that takes practice. We used the website to guide our session today. I asked the student to watch the videos and do the practice problems for what we have covered so far which is limits and derivatives. I also recommended that he look at the pre-calculus tutorial online and review anything that's unfamiliar. He is learning the basics of calculus very quickly, but his algebra and trigonometry is a little bit rusty since he hasn't taken math in over a year."