Evaluate the limit of sinx over x

The video tutorial discusses the limitations of graphing calculators in identifying holes and asymptotes. It emphasizes the importance of understanding these concepts fundamentally. The tutorial explains how to use scientific calculators to calculate limits by choosing values close to zero and testing both left and right limits. The example provided shows that as values approach zero, the result approaches one, confirming the limit.

Why is it important to understand the concepts of holes and asymptotes even when using a graphing calculator?

• Because graphing calculators can show all details of a graph.

• Because graphing calculators do not display holes and asymptotes.

• Because graphing calculators can solve all mathematical problems.

• Because graphing calculators are always accurate.

What is a key indicator of a hole in a graph when using a graphing calculator?

• A continuous line without breaks.

• A value that is defined.

• A sharp turn in the graph.

• A value that is undefined.

How can you approximate the limit of a function as X approaches zero?

• By using values that are far from zero.

• By using values that are close to zero.

• By using only positive values.

• By using only negative values.

What should you do to ensure the limit is the same from both sides of a point?

• Ignore the sides and focus on the center.

• Test both the left and right sides of the point.

• Test only the left side of the point.

• Test only the right side of the point.

What does the limit of a function as X approaches zero indicate if both sides approach the same value?

• The function has an asymptote at zero.

• The function is continuous at zero.

• The function is undefined at zero.

• The function has a hole at zero.