## Derivative

Definition as the limit of a difference quotient.

18.01

*Single Variable Calculus,*Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

## Difference Quotient Definition of Derivative

Finding the derivative of f(ax) using the difference quotient definition of derivative.

18.01

*Single Variable Calculus,*Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

- Complete practice problem 3 on page 2
- Check solution to practice problem 3 on page 11

## Derivative as Limit of Difference Quotients

18.01

*Single Variable Calculus,*Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

Finding the derivative of a function by taking the limit of a difference quotient.

- Complete exam problem 1 on page 2
- Check solution to exam problem 1 on page 1

Two problems which involve evaluating a derivative using the limit definition of a derivative.

- Complete exam problems 1.3 and 1.4 on page 1
- Check solution to exam problems 1.3 and 1.4 on page 1

## Limit Definition of Derivative

18.01

*Single Variable Calculus,*Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

Finding the derivative of x^{3} using the limit definition of a derivative.

- Complete exam problem 2 on page 1
- Check solution to exam problem 2 on page 2

Finding the derivative of 1/x^{2} using the limit definition of a derivative.

- Complete exam problem 3 on page 1
- Check solution to exam problem 3 on page 1

Finding the derivative of a function using the limit definition of a derivative

- Complete exam problem 7 on page 2
- Check solution to exam problem 7 on page 2

## Limits and Derivatives

18.01

*Single Variable Calculus,*Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

Evaluating a limit by relating it to a derivative.

- Complete exam problem 3 on page 1
- Check solution to exam problem 3 on page 2

Evaluating two limits by relating them to derivatives.

- Complete exam problem 6 on page 2
- Check solution to exam problem 6 on page 2

## Slope and Derivative

Six questions involving the definition of a derivative as the limit of a difference quotient, tangent lines to a function at a point, and drawing graphs of the derivatives of functions given in graph form.

18.01

*Single Variable Calculus,*Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

- Complete exam problem 1C–1 on page 2 to problem 1C–6 on page 3
- Check solution to exam problems on pages 4–6