Math 100:V02, Winter Term 2024
Pre-Midterm Sheet
February 8, 2024
Material
The material for midterm 1 consists of the material covered in the lectures up Taylor
expansion (discussed in lecture on Feburary 8), including
- The ladder of functions, asymptotics at ∞, asymptotics at 0, asymptotics
at a.
- Limits, one-sided limits, blow-up and limits in the extended sense, limits
at infinity.
- The linear approximation and the definition of the derivative,
- Continuity: gluing functions and derivatives.
- Differentiation rules: linearity, product rule, quotient rule, chain rule.
Partial derivatives.
- Differentiation table: exponentials, logarithms, trigonometric functions
- Exponential growth and decay: finding solutions to the equation y′ = ry.
- Applications of the chain rule: implicit diffeerentiation and related rates.
- Shape of the curve: increase/decrease, concavity and convexity.
- Taylor expansion: definition of the expansion, computing by repeated
differentiation, reading off coefficients.
Structure
This midterm is about mastering the basic skills of this course.
- The exam will last 50 minutes and consist of 15 questions, which will be
marked correct/incorrect based on the final answer only.
- Students are required to score at least 80% (12/15) to pass the course.
- There will be three retakes, the last of which will be a section of the final
exam.
For practice problems use worksheets, as well as the CLP problem book and
Schaum’s Outline of Theory and Problems of Differential and Integral Calculus
.
Practicalities
The exam will take place during class on Thursday, February 15.