Calculus Intro and Limits

Which of these problems requires calculus to solve?

• Instantaneous rate of change at a point

• Slope of a line

• Are of a rectangle

• Area Under a Curve

• Length of an Arc

Tags

CCSS.8.EE.B.5

The slope of a tangent line

• Always equal to the slope of the secant line

• Limit of the slope of the secant lines

• Equal to the area under a curve

• Limit of the area of the rectangle

Finding the area of a plane bounded by functions cannot be solved with Calculus.

• True
• False

Which of these are examples of limits that fail to exist?

• Different right and left limits

• Unbounded

• Numerical LImit

• Oscillating

A limit cannot exists if the function is undefined at that point.

• True
• False

What is the fundamental difference between precalculus and calculus?

• Precalculus is dynamic, calculus is static.

• Precalculus deals with change, calculus deals with constants.

• Precalculus is more static, and calculus is more dynamic.

• Precalculus uses numbers, calculus uses letters.

What is calculus often referred to as, based on its three stages (Precalculus mathematics → Limit process → Calculus)?

• A "static system"

• A "limit machine"

• A "constant calculator"

• A "precalculus enhancer"

Which of the following is identified as a basic problem in calculus?

• The quadratic equation problem

• The tangent line problem

• The constant velocity problem

• The circle curvature problem

In the context of the tangent line problem, what type of line is used to approximate the slope of the tangent line by passing through the point of tangency and a second point on the curve?

• A perpendicular line

• A horizontal line

• A secant line

• A vertical line

How is the slope of the tangent line defined when a "limiting position" of the secant lines exists?

• As the average of the secant slopes.

• As the sum of the secant slopes.

• As the product of the secant slopes.

• As the limit of the slopes of the secant lines.

Tags

CCSS.8.EE.B.5