Understanding One-Sided Limits

The video tutorial explains the concept of one-sided limits using graphical representations. It emphasizes the importance of notation in determining limits and demonstrates how to find limits as x approaches a specific value from the left or right. The tutorial also discusses the impact of piecewise functions on limit determination and provides examples of limits approaching x = 2 from different sides. The video concludes with a preview of upcoming topics on one-sided limits and limits at infinity.

What is the significance of notation in determining one-sided limits?

• It determines the continuity of the function.

• It shows the exact value of the limit.

• It indicates the direction from which a value is approached.

• It helps in identifying the function value at a point.

When approaching -2 from the negative side, what is the function value?

• 1

• 2

• -1

• 0

What is the function value when approaching -2 from the positive side?

• 0

• 1

• -1

• 2

Why does the double-sided limit at -2 not exist?

• The graph is discontinuous.

• The function value is zero.

• The left and right limits are not equal.

• The function is not defined at -2.

What is the left-sided limit when approaching 2?

• 0

• -1

• 1

• 2

What is the right-sided limit when approaching 2?

• -1

• 1

• 0

• 2

What is the limit as x approaches 2 from both sides?

• 0

• 1

• 2

• -1

What is the function value when approaching 2 from the left side?

• -1

• 2

• 0

• 1

What is the function value when approaching 2 from the right side?

• 2

• -1

• 1

• 0

Why do the limits exist even if the function does not exist at a point?

• Because the function is continuous.

• Because the function value is zero.

• Because limits are about approaching values, not actual values.

• Because the graph is smooth.