Topics for the First Midterm

Functions

• domain and range
• composition of functions
• trig functions
• inverses

Exponentials and Logarithms

• definition of the number e
• graphs of exponentials and logarithms
• laws of exponentials and logarithms

Tangents and Velocities

• average velocity; instantaneous velocity
• secant lines; tangent lines

Limits of Functions

• definition of limit (in words and the relation to a graph)
• right- and left-hand limits
• limit laws
• computing limits using algebra
• infinite limits and vertical asymptotes
• The Squeeze Theorem

Continuity

• definition of continuity
• removable discontinuities
• The Intermediate Value Theorem

Limits at Infinity

• computing limits as x approaches + infinity or - infinity
• horizontal asymptotes

Tangent lines

• definition of the slope of a tangent line
• finding equations of tangent lines