Continuity

Question 1

What does it mean for a function to be continuous at a point?

Answer 1

Question 2

What are the different types of discontinuities?

Answer 2

Question 3

What does it mean for a function to be continuous on an interval?

Answer 3

Question 4

How does the Intermediate Value Theorem relate to continuity?

Answer 4

Question 5

What steps do you take to check the continuity of a function at a point?

Answer 5

Question 6

Are polynomials and rational functions continuous?

Answer 6

Polynomials are continuous for all real numbers. Rational functions are continuous wherever their denominators are non-zero.

Question 7

How do you determine the continuity of a piecewise function?

Answer 7

To determine the continuity of a piecewise function, check the continuity at each point where the function changes its formula, particularly at the boundaries where the pieces meet.

Question 8

If two functions are continuous, is their composition also continuous?

Answer 8

Question 9

How is continuity related to limits?

Answer 9

Question 10

Are trigonometric functions continuous?

Answer 10