1.1.2 The Two Questions of Calculus

Question 1

The Two Questions of Calculus

Answer 1

• Use calculus to find instantaneous rates of change and areas of exotic shapes.
• Average rate of change: r = d/t

Question 2

rate of change and differential calculus

Answer 2

• Calculus creates a connection between two very different problems.
• The first problem deals with the instantaneous rate of change of an object in motion. An object’s average rate of change (or velocity) is equal to the change in distance divided by the change in time.
• But suppose you need to know the velocity of an object at an exact moment in time? Then the change in time would be 0. Division by 0 is not defined.
• Differential calculus seeks to resolve this issue. In fact, the formula for average rate of change is the very heart of differential calculus

Question 3

integral calculus

Answer 3

• Differential calculus is only one piece of this course.
• The second piece is called integral calculus. In integral
  calculus you will learn how to find the areas of different
  shapes, particularly exotic shapes that do not have simple area formulas.
• It turns out that both of these applications involve calculus and that the two answers are related to each other! By the end of this course you will understand how.