A PREVIEW OF CALCULUS

A PREVIEW OF CALCULUSSection 1.1

When you have finished your homework you should be able

to…• Understand what calculus is and

how it compares with precalculus• Understand that the tangent line

problem is basic to calculus• Understand that the area problem

is also basic to calculus

Find the area of the triangle with vertices Round to the nearest hundredth.

1,2 , 2,3 , 0,6 .

WHAT IS CALCULUS?

1

1ln , 0

x

x dt xt

0.

Consider the following function.

Using tools you learned in precalculus, what can you tell me about this function?

0.

0.

23 5 2f x x x

CALCULUS IS THE MATHEMATICS OF

CHANGE

0.

Think of calculus as a “limit machine” with 3 stages1st Stage: Precalculus mathematics

Example:The slope of a lineThe area of a

rectangle2nd Stage: Limit Process3rd Stage: A new calculus Formation

Example:DerivativeIntegral

Determine if the following problem is solved using precalculus or calculus.

Find the slope of the secant line of a curve.

A. PrecalculusB. Calculus

Determine if the following problem is solved using precalculus or calculus.

Find the area bounded by the graph of , the x-axis, and

the lines and .

A. PrecalculusB. Calculus

3x

2y x1x

THE TANGENT LINE PROBLEM

• What You are Given:– A function – A point on its graph

• What You are Asked to Find:– An equation of the tangent line to the graph

at the point • With the exception of vertical lines, this

is equivalent to finding the SLOPE of the tangent line at x.

– You can approximate this slope by using the point of tangency and a second point on the curve. Such a line is called a secant line

THE AREA PROBLEM– What you are asked to find:

• The area of a plane region that is bounded by the graph of functions