Examples of removable and non removable discontinuities to find limits

The video tutorial covers the evaluation of limits in piecewise functions, focusing on determining continuity by checking left and right-hand limits. It explains how to use factoring techniques, such as the difference of squares, to evaluate limits and identify removable discontinuities. The tutorial also discusses nonremovable discontinuities that lead to asymptotes, emphasizing the importance of understanding graph behavior. The session concludes with a brief introduction to a quiz to reinforce the concepts learned.

What is the key method to determine if a piecewise function is continuous?

• Check if the function is differentiable

• Evaluate the function at zero

• Use the mean value theorem

• Check the left and right-hand limits

When direct substitution is not possible, which technique can be used to evaluate limits?

• Factoring techniques

• Using L'Hôpital's rule

• Completing the square

• Integration by parts

What type of discontinuity is created when a factor can be divided out?

• Oscillating discontinuity

• Removable hole

• Infinite discontinuity

• Jump discontinuity

What results in an asymptote in a function?

• A zero in the numerator

• A constant term in the function

• A factor that cannot be divided out

• A factor that can be divided out

What happens to the graph of a function at a non-removable discontinuity?

• It forms a hole

• It becomes continuous

• It oscillates infinitely

• It approaches an asymptote