#### Content for the First Exam

#### Linear approximation

We use a method called “linear approximation” to estimate the value of a
(complicated) function at a given point.

#### Computations for graphing functions

We will give some general guidelines for sketching the plot of a function.

#### Implicit differentiation

In this section we differentiate equations that contain more than one variable on one
side.

#### Finding dx dy

In this section we differentiate equations without expressing them in terms of a single
variable.

#### Content for the Second Exam

#### Derivatives of inverse trigonometric functions BreakGround

Two young mathematicians think about the plots of functions.

#### Derivatives of inverse trigonometric functions

We derive the derivatives of inverse trigonometric functions using implicit
differentiation.

#### The Inverse Function Theorem

We see the theoretical underpinning of finding the derivative of an inverse function at
a point.

#### Indeterminate mutterings

Two young mathematicians consider a way to compute limits using derivatives.

#### Content for the Third Exam

#### Approximating area with rectangles

We introduce the basic idea of using rectangles to approximate the area under a
curve.

#### The First Fundamental Theorem of Calculus

The rate that accumulated area under a curve grows is described identically by that
curve.

#### The Second Fundamental Theorem of Calculus

The accumulation of a rate is given by the change in the amount.