Expert Math Tutor with 5+ years of experience teaching High School and University Students

The Tutor and Student extensively practiced L'Hôpital's Rule for evaluating indeterminate limits. They covered various indeterminate forms, demonstrated how to transform them, and applied the rule through multiple examples involving different functions. The Tutor also provided practice problems as homework.

The tutor and student worked through various limit evaluation techniques, including those involving absolute values, factorization (specifically difference of squares), and trigonometric approximations near zero. The student practiced algebraic manipulation and simplification to find limit values, and they discussed common errors related to fractions and trigonometric functions.

The Student and Tutor discussed derivatives of inverse functions, including both explicit and implicit differentiation methods. The Student practiced applying these methods to various functions, including trigonometric functions, and was assigned homework problems for further practice. The session included strategies for evaluating inverse trigonometric functions using right triangles.

The Student and Tutor explored the concept of limits in calculus, covering direct evaluation for various function types, including polynomial, radical, trigonometric, and absolute value functions. They also delved into one-sided limits, piecewise functions, and special functions like floor and ceiling functions, discussing when limits exist and when they do not. The next session will focus on removable discontinuities and advanced limit techniques.

The tutor and student reviewed various calculus topics, including limits at infinity, basic and advanced derivatives (power rule, quotient rule, chain rule, implicit differentiation, second derivatives), and an introduction to related rates and linearization. They practiced identifying appropriate rules and solving problems, with a plan to cover more on linearization later.

The tutor and student worked through the limit definition of the derivative using algebraic examples. They practiced applying the formula, simplifying expressions, and evaluating limits for linear, quadratic, and radical functions. Future sessions were tentatively scheduled to cover the broader calculus curriculum.