Learn how to evaluate the limit of a piecewise function

The video tutorial explains the concept of continuity in graphs and how to evaluate limits. It emphasizes the importance of ensuring that the left-hand and right-hand limits are equal for a limit to exist. The tutorial also covers the use of direct substitution to evaluate limits when dealing with continuous functions, providing a step-by-step example to illustrate the process.

What is a key indicator that a function is not continuous when looking at a graph?

• The graph is below the x-axis.

• The graph is above the x-axis.

• The graph has a hole or break.

• The graph is a straight line.

What must be true for a function to be continuous at a point?

• The left-hand limit must be zero.

• The left-hand limit must equal the right-hand limit.

• The left-hand limit must be less than the right-hand limit.

• The left-hand limit must be greater than the right-hand limit.

What method can be used to evaluate limits for continuous functions?

• Graphical analysis

• Direct substitution

• Numerical approximation

• Differentiation

In the example provided, what was the left-hand limit when x approaches 2?

• 0

• 3

• 2

• 1

Why does the limit not exist in the given example?

• The graph is a straight line.

• The function is continuous at x = 2.

• The left-hand and right-hand limits are not equal.

• The function is not defined at x = 2.