Calculus Lecture: Understanding Velocity and Tangent Lines

These flashcards cover key vocabulary and concepts related to calculus, particularly focusing on velocity, secant and tangent lines, and their applications in analyzing motion.

What is Calculus?

The study of change, including concepts like limits, derivatives, and integrals.

Secant line

A line that intersects a curve at a minimum of two distinct points.

Tangent line

A line that touches a curve at one point and is parallel to the curve at that point.

Difference quotient

The expression f(a + h) − f(a) / h, representing the slope of the secant line between two points on a function.

Average velocity

The total displacement divided by the total time taken.

Instantaneous velocity

The velocity of an object at a specific moment in time.

Position function

A mathematical function that describes the location of an object over time, denoted as s(t) in this context.

How to approximate instantaneous velocity

By calculating the slope of the secant lines as the time intervals get smaller.

Usain Bolt's average velocity in the 100 meter dash

Calculated using the formula distance/time, resulting in approximately 10.34 m/s.

Tangent line to a function

A line that represents the best linear approximation to the function at a given point.