Final Study guide for Math 220 GE1.
Chapters 1-3
Basics of functions
- Trigonometric functions: Know the graphs and behaviour of sin(x) and
cos(x), including their domains and ranges and the values they take at the
“celebrated” angles. You should also know the definitions of the other trig
functions (e.g., tan(x) = sin(x)
cos(x)).
- Logs and Exponentials: Know the graphs and behaviour of ex, ln(x), and
related functionsm including their domains and ranges. You should know the
relation between values of logs and the corresponding exponential functions.
- Inverse functions: You should know how to find the formulas for and do-
mains of inverse functions, as well as their derivatives. Remember: f−1(x) is
NOT 1/f(x)!
Basics of Derivatives
- Know the limit definition of the derivative.
- Know the relationships between the behavior of the function and its deriva-
tives (e.g., f′′(x) positive means f(x) is concave up).
- Know how to classify stationary points using the First and Second Deriva-
tive Tests. You may be asked to state one or both.
- Know the derivative formulas for xk,sin(x),cos(x), bx,logb(x),and inverse
trig functions.
- Be able to use the product rule, quotient rule, and chain rule.
- Be able to perform implicit differentiation.
- Know how to find the line tangent to a curve at a point.
Differential Equations
- You should know how to solve the elementary differential equations we cov-
ered in class. Specifically: those solveable by antidifferentiating both sides,
those in the form y′=ky, and those in the form y′′ =−ky . You should know
the general formula for the solutions of these last two.
- You should know how to use initial values to find exact solutions.
- You should know what an IVP is and be able to write one down from a
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