Calculus I – Coming Soon
Limits, derivatives, and integrals with applications. Rates of change, tangents, areas, and volumes of revolution.

16
Video
Lessons
Table of Contents
Tangent Lines and Secant Lines
 Explain what a tangent line is
 Explain what a secant line is
 Describe the relationship between secant lines and tangent lines
 Find an equation of a tangent line
Average and Instantaneous Velocity
 Describe the connection between secant and tangent lines and velocity
 Calculate average velocity
 Estimate instantaneous velocity
The Limit of a Function
 Explain what a limit is
 Estimate the limit of a function
The Squeeze Theorem
 State the Squeeze Theorem
 Use the Squeeze Theorem to compute limits
Continuity
 Explain what it means for a function to be continuous at a point
 Explain what it means for a function to be continuous from the left or right
 Explains what it means for a function to be continuous on an interval
 Show a function is continuous at a point, from the left/right, or over an interval by using the definition of continuity
The Intermediate Value Theorem
 Explain the Intermediate Value Theorem
 Use the Intermediate Value Theorem to show that a function has a root
Limits at Infinity
 Explain what a limit at infinity is
 Find limits at infinity
Horizontal Asymptotes
 Describe a horizontal asymptote
 Find horizontal asymptotes
Infinite Limits at Infinity
 Explain the meaning of $\lim_{x \to \infty} f(x) = \infty$
 Evaluate limits that are infinite at infinity
The Derivative of e^x
 Differentiate the natural exponential function without using the limit definition of the derivative
Euler’s Constant
 Define the number e
The Product Rule
 Take the derivative of a product of functions
The Quotient Rule
 Take the derivative of a quotient of functions
Combining the Product and Quotient Rules
 Take the derivative of a function using both the product rule and the quotient rule
Derivatives of General Exponential Functions
 Find the derivative of b^x for b > 0
 Take the derivative of functions that include b^x
Linear Approximation
 Define the linearization of a function f at a
 Find the linearization of f at a