Limits and Continuity Concepts

The video tutorial explains the concept of limits, focusing on one-sided limits and their connection to vertical asymptotes. It provides examples using the tangent function, analyzing limits as x approaches PI/2 and 3PI/2, demonstrating how these limits relate to vertical asymptotes. The tutorial concludes with a regular limit example as x approaches PI, showing how the function value is approached from both sides.

What is a vertical asymptote in the context of limits?

• A line the graph crosses at infinity

• A point where the graph crosses the y-axis

• A line the graph approaches but never crosses

• A point where the graph crosses the x-axis

What happens to the function values as x approaches π/2 from the left for tangent x?

• They remain constant

• They decrease without bound

• They approach zero

• They increase without bound

How can we verify the limit as x approaches π/2 using a table of values?

• By checking if the values approach zero

• By checking if the values remain constant

• By checking if the values increase without bound

• By checking if the values decrease

What is the approximate value of π/2 in decimal form?

• 6.2832

• 4.7124

• 3.1416

• 1.5708

As x approaches 3π/2 from the left for tangent x, what do the function values do?

• They approach zero

• They decrease without bound

• They increase without bound

• They remain constant

What is the approximate value of 3π/2 in decimal form?

• 3.1416

• 1.5708

• 6.2832

• 4.7124

What must happen for a regular limit to exist as x approaches a point?

• The function must approach the same value from both sides

• The function must be discontinuous at that point

• The function must be undefined at that point

• The function must approach different values from left and right

What is the value of tangent π?

• 0

• -1

• 1

• Infinity

What does it mean if a function is continuous around a value?

• The function is undefined at that value

• The function has a jump at that value

• The function can be directly substituted at that value

• The function has a hole at that value

What is the significance of a limit equaling positive infinity?

• The function is continuous

• The limit does not exist

• The limit exists

• The function is differentiable