### Calculus I – Coming Soon

Limits, derivatives, and integrals with applications. Rates of change, tangents, areas, and volumes of revolution.

• 16 Video
Lessons
##### 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