Calculus Challenge Exam Topics
1. Functions and Graphs
- Combinations of functions, including composites, transformations
- Trigonometric functions
- Inverse trig functions
- Hyperbolic functions
- Exponential and logarithmic functions
- Limit laws
- Continuity
- Limits at infinity and horizontal asymptotes
- Infinite limits and vertical asymptotes
- Indeterminate forms and L'Hospital's rule
- Definition of the derivative, calculation from the definition
- Tangent lines
- Derivative rules: product, quotient, chain rules
- Derivatives of trig and inverse trig functions
- Derivatives of exponential and logarithmic functions
- Derivatives of hyperbolic functions
- Implicit differentiation
- Logarithmic differentiation
- Basic integration formulas (from known derivatives)
- Rates of change, examples in natural and social sciences, position-velocity-acceleration
- Related rates
- Local/absolute extrema
- Curve sketching
- Optimization
- Intermediate Value Theorem
- Extreme Value Theorem
- Rolle's Theorem and Mean Value Theorem