1.4 Estimating Limit Values from Tables

• What does a limit describe as the input approaches a certain number?

  The function's value
• As \(x\) approaches 2, the function \(f(x) = \frac{x^2 - 4}{x - 2}\) approaches 4
• Creating a table is essential for estimating limit values from numerical data.
• Steps for creating a table to estimate limit values

  1️⃣ Choose x-values close to the target limit

  2️⃣ Evaluate f(x) for each x-value

  3️⃣ Organize data in a table with x and f(x) columns
• What is the estimated limit of \(f(x) = x^2 - 5x + 6\) as \(x\) approaches 3?

  0
• From the table, we estimate \(\lim_{x \to 3} f(x) = 0
• To estimate a limit from a table, one must choose x-values near the target limit.
• What is the estimated limit of \(f(x) = \frac{x^2 - 4}{x - 2}\) as \(x\) approaches 2?

  4
• As \(x\) approaches 2, the function \(f(x) = \frac{x^2 - 4}{x - 2}\) approaches 4
• Steps for estimating a limit from a table

  1️⃣ Choose x-values near the target limit

  2️⃣ Evaluate f(x) for each x-value

  3️⃣ Organize data in a table

  4️⃣ Analyze the trend as x approaches the target
• Creating a table for limit estimation involves organizing data in a table format.
• Organize the data in a table with the x-values in one column and the corresponding \(f(x)\) values in another column
• To estimate the limit \(\lim_{x \to 3} f(x)\) where \(f(x) = x^2 - 5x + 6\), we can create a table
• When creating a table for limit estimation, you should choose x-values that are close to the target limit.
• For each chosen x-value, you must evaluate the function f(x)
• Steps to create a table for estimating limit values

  1️⃣ Choose x-values close to the target limit

  2️⃣ Evaluate the function f(x) for each x-value

  3️⃣ Organize the data in a table format
• The x-values and f(x) values should be organized in separate columns of the table.
• By analyzing the trend in the f(x) values as x approaches 3, we can estimate the limit to be 0
• When estimating a limit from a table, you should choose x-values that are close to the target value.
• Steps to estimate a limit from a table

  1️⃣ Choose x-values close to the target

  2️⃣ Evaluate f(x) for each x-value

  3️⃣ Organize data in a table

  4️⃣ Analyze the trend as x approaches the target
• As x approaches 2, f(x) approaches 4
• When estimating a limit from a table, it is necessary to choose x-values both smaller and larger than the target limit.
• By analyzing the trend in the f(x) values as x approaches 2, we can estimate the limit to be 4