Exploring Limits of Functions

What is the main purpose of using limits in calculus?

• To determine the value a function is approaching

• To find the exact value of a function

• To solve equations

• To find the maximum value of a function

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CCSS.HSF.IF.C.7

In the pizza analogy, what does the fridge represent?

• The exact value of the function

• The input value

• The value the function is approaching

• The output value

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CCSS.HSF.IF.A.1

What value does the function f(x) = 3x^2 - 1 approach as x gets close to 2?

• 12

• 11

• 10

• 9

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CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Why is it important to focus on the value a function is approaching rather than the value it reaches?

• Because it is more accurate

• Because the function might not reach the value it is approaching

• Because the function always reaches the same value

• Because it is easier to calculate

In the second pizza analogy, what does the missing fridge represent?

• A function with no limit

• A function that does not reach its limit

• A function that reaches its limit

• A function with multiple limits

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CCSS.HSA.SSE.A.1

What happens when you plug x = 2 into the function (x^2 - 4) / (x - 2)?

• You get an undefined value

• You get a value of 0

• You get a value of 4

• You get a value of 2

What value does the function (x^2 - 4) / (x - 2) approach as x gets close to 2?

• 3

• 4

• 5

• 6

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CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

What does the hole in the graph of (x^2 - 4) / (x - 2) at x = 2 represent?

• The function does not reach 4

• The function reaches 4

• The function is undefined at 4

• The function has no limit

What will be introduced in the next video to explain the concept of 'arbitrarily close'?

• Derivatives and integrals

• Limits and continuity

• Functions and graphs

• Epsilon and delta

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