0.1 Calculus: Big Ideas

Question 1

What is Calculus?

Answer 1

The study of change. Exploring how functions change at a moment or over time.

Question 2

Basically, what is a derivative?

Answer 2

An instantaneous rate of change. Ex. At t = 1, how fast is this function changing?

Question 3

Graphically, what is a derivative?

Answer 3

The slope of the tangent line to a curve at a specific point.

Question 4

How does a derivative use limits?

Answer 4

To find slope, you need two points but we want the slope at one point, so we use a limit to make the distance between our points be 0.

Question 5

Basically, what is an integral?

Answer 5

An accumulation of change. Ex. From t = 1 to t = 5, how much did this function increase?

Question 6

Graphically, what is an integral?

Answer 6

The area under a portion of a curve.

Question 7

How does an integral use limits?

Answer 7

We want to use something simple like rectangles to find a curvy area but they aren’t actually rectangles. If we use limits to make the rectangles infinitesimally thin or make an infinite number of rectangles, the approximation will become the actual area.