Review for First Exam (0.1 - 3.2)
Major Concepts
- Plotting functions (shifting, scaling, reflecting)
- Orthogonality and inner product
- Finding parametric representations for curves
- Limits and Continuity
- Limits and Differentiability
- Rules for Differentiation
Key Concepts
- Composition of 2 functions
- Pythagorean theorem
- Qualitative and Quantitative understanding of the limit
process
- Computing the angle between two vectors (Law of Cosines)
- Orthogonality - given one vector, compute another vector
perpendicular to it
- Scalar and vector projections (memorize formula if necessary)
- Scalar (inner, dot) product
- Compute distance from point to a line
(reduces to 2 equations in 2 unknowns)
- Cartesian vs Parametric form for curves - conversion from
one form to another
- Point-Slope form of the Line - given a slope, and a point
on a line, compute the formula for the line
- Finding equation of tangent line in two-dimensions (point-slope)
- Finding equation of tangent line in more than two dimensions
(tangent-vector parameterization)
- When do limits exist?
- What to do if 0/0 occurs in a limit
- Average vs. instantaneous velocity (slope of secant vs tangent)
- Physical interpretation of derivative as velocity or rate
of change
- One-sided vs. Two-sided limits
- Use of the limit laws
- Applications of the squeeze theorem
- Application of Intermediate Value Theorem, e.g. finding zeroes (roots)
of a function
- Limits and continuity
- When is a function continuous at a point? Cases where
it is not.
- Horizontal Asymptotes - Limit criteria
- Vertical Asymptotes- Limit criteria
- Computing the derivative from the limit definition
- Limits and differentiability
- When is a function differentiable at a point? Cases where
it is not.
- Product rule, quotient rule (for differentiation)
- Definition of work - simple examples