1.4 Estimating Limit Values from Tables

    Cards (60)

    • What does a limit tell us about a function's behavior?
      Value as input approaches
    • As xx approaches 2, f(x)f(x) approaches 4
    • The limit of f(x)f(x) as xx approaches 2 is written as limx2f(x)=\lim_{x \to 2} f(x) =4 4.
    • What is the function f(x)=f(x) =x2+ x^{2} +2 2 equal to when x=x =0 0?

      2
    • Steps to estimate a limit from a table
      1️⃣ Examine values from the left
      2️⃣ Examine values from the right
      3️⃣ Determine the common approach
    • What do we examine to estimate limits?
      Function values
    • To estimate limits, we examine the values of a function as it approaches a target point from both the left and the right
    • Estimating limits involves examining function values as xx approaches a target point from only one direction.

      False
    • What value does f(x)f(x) approach as xx approaches 2 from the left in the given table?

      4
    • As xx approaches 2 from the right, f(x)f(x) approaches the value of 4
    • From the given table, \lim_{x \to 2} f(x) =4</latex>.
    • Steps to estimate the limit of f(x)=f(x) =x2+ x^{2} +2 2 as xx approaches 0.

      1️⃣ Choose values of xx near 0 from the left and right
      2️⃣ Evaluate f(x)f(x) for these xx values
      3️⃣ Observe the trend in f(x)f(x)
      4️⃣ Conclude the limit value
    • What is the function given in the example for estimating limits?
      f(x)=f(x) =x2+ x^{2} +2 2
    • What do we examine to estimate limits of a function?
      Function values from left and right
    • As xx approaches 2 from the left, f(x)f(x) approaches 4
    • If f(x)f(x) approaches 4 as xx approaches 2 from both sides, then \lim_{x \to 2} f(x) = 4</latex>.
    • For f(x)=f(x) =x2+ x^{2} +2 2, what value does f(x)f(x) approach as xx approaches 0?

      2
    • What two directions do we examine to estimate limits?
      Left and right
    • As xx approaches 2 from the left, f(x)f(x) approaches 4
    • What is the function used in the example to estimate the limit as xx approaches 0?

      f(x)=f(x) =x2+ x^{2} +2 2
    • To estimate limits, we only need to examine values approaching from the left.
      False
    • As xx approaches 2 from the right, f(x)f(x) approaches 4
    • What is the value of f(x)=f(x) =x2+ x^{2} +2 2 when x=x =0.1 - 0.1?

      2.012.01
    • We can estimate limits by examining values of a function as it approaches a target point from both the left and right.
    • Match the value of xx with the corresponding value of f(x)f(x) when limx2f(x)=\lim_{x \to 2} f(x) =4 4:

      1.91.9 ↔️ 3.83.8
      1.991.99 ↔️ 3.983.98
      2.012.01 ↔️ 4.024.02
      2.12.1 ↔️ 4.24.2
    • What is the limit of f(x) = x^{2} + 2</latex> as xx approaches 0?

      limx0f(x)=\lim_{x \to 0} f(x) =2 2
    • Estimating limits involves analyzing the behavior of a function as it approaches a specific point from both the left and right.
    • To estimate limits, we examine the values of a function as it approaches a target point from the left and right
    • Match the value of xx with the corresponding value of f(x)f(x) when limx0f(x)=\lim_{x \to 0} f(x) =2 2:

      0.1- 0.1 ↔️ 2.012.01
      0.01- 0.01 ↔️ 2.00012.0001
      00 ↔️ 22
    • How does the example function f(x)=f(x) =x2+ x^{2} +2 2 behave as xx approaches 0 from the left?

      Approaches 2
    • Estimating limits requires examining only the values of f(x)f(x) as xx approaches the target point from the left.

      False
    • As xx approaches 2 from the left, f(x)f(x) approaches 4
    • Order the steps to estimate a limit using values approaching from the left and right.
      1️⃣ Choose a target point xx.
      2️⃣ Examine values of f(x)f(x) as xx approaches from the left.
      3️⃣ Examine values of f(x)f(x) as xx approaches from the right.
      4️⃣ Determine the value f(x)f(x) approaches from both sides.
    • What is the limit of f(x)=f(x) =x2+ x^{2} +2 2 as xx approaches 0 from the right?

      limx0f(x)=\lim_{x \to 0} f(x) =2 2
    • To estimate limits, we must always create a table of values to analyze.
      False
    • As xx approaches 2 from the right, f(x)f(x) approaches 4
    • What values of xx are used to estimate the limit of f(x)=f(x) =x2+ x^{2} +2 2 as xx approaches 0?

      0.1- 0.1, 0.01- 0.01, 0
    • What value does f(x)f(x) approach as xx approaches 2 from the left?

      4
    • What is the function given as an example to estimate a limit?
      f(x)=f(x) =x2+ x^{2} +2 2
    • For f(x) = x^{2} + 2</latex>, as xx approaches 0, f(x)f(x) approaches 2
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