Limits & Continuity Review

Let f be a continuous function for which f(-2)=1 and f(5)=-3. The Intermediate Value Theorem guarantees that

• f(c)=2 for at least one c between -3 and 1

• f(c)=0 for at least one c between -2 and 5

• f(c)=0 for at least one c between -3 and 1

• f(c)=2 for at least one c between -2 and 5

• I only

• II only

• I, II, III

• None

• 2
• -3/4
• -1/3
• 1/4

• 8

• 10/3

• -7

• 3/10

• 4

• -2

• 2

• 16

What is the Limit Existence Theorem?

• The limit from the left

• The limit exists

• If the limit from the left equals the limit from the right, then the overall limit exists.

• One sided limits are from the left if there is a negative sign and from the right if its a plus sign

What is continuity?

• Removable discontinuity

• Drawing a function without picking up your pencil from the paper

• Non-removable discontinuity

• Jump discontinuity

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Which statement is true?

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