Understanding Continuity at a Point

The video tutorial explores the concept of continuity at a point through three examples. It discusses how to determine if a function is defined at a point, whether the limit exists, and if the function is continuous. The first example examines continuity at X = -3, where the function is defined but not continuous due to differing limits from both sides. The second example looks at X = 4, where the function is defined but not continuous as the limit does not equal the function value. The final example at X = 2 shows a continuous function as all conditions are met. The tutorial concludes with the conditions required for continuity.

What is the function value at x = -3?

• -5

• 2

• 5

• 0

Does the limit as x approaches -3 exist?

• Yes, it is 5

• Yes, it is 2

• No, it does not exist

• Yes, it is -5

Is the function continuous at x = -3?

• Only from the left

• Yes

• No

• Only from the right

What is the function value at x = 4?

• 0

• 2

• -4

• 4

What is the limit as x approaches 4?

• 0

• -4

• 4

• 2

Is the function continuous at x = 4?

• Yes

• No

• Only from the right

• Only from the left

What is the function value at x = 2?

• 0

• 2

• -3

• 3

Does the limit as x approaches 2 exist?

• Yes, it is -3

• Yes, it is 0

• No, it does not exist

• Yes, it is 3

Is the function continuous at x = 2?

• No

• Yes

• Only from the left

• Only from the right

What are the conditions for a function to be continuous at a point?

• Function is not defined, limit exists, limit equals function value

• Function is defined, limit does not exist, limit equals function value

• Function is defined, limit exists, limit equals function value

• Function is defined, limit exists, limit does not equal function value