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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

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