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Create a table of value (use 8 values - 4 on the left and 4 on the right) and a calculator to the estimate the limit if it exist. Round off all values to 4 decimals places. lim √10-x-4 x36 x + 6

Create a table of value (use 8 values - 4 on the left and 4 on the right) and a calculator to the estimate the limit if it exist. Round off all values to 4 decimals places. lim √10-x-4 x36 x + 6

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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**Calculating the Limit Using a Table of Values** To estimate the limit of the function as \( x \) approaches 6, create a table of values using 8 values—4 values approaching 6 from the left and 4 values approaching 6 from the right. Use a calculator to determine and round off all values to 4 decimal places. The function to be evaluated is: $$ \lim_{{x \to 6}} \frac{\sqrt{10 - x} - 4}{{x - 6}} $$ ### Steps: 1. Choose 4 values of \( x \) slightly less than 6. 2. Choose 4 values of \( x \) slightly greater than 6. 3. Evaluate the function for each chosen \( x \). 4. Round the calculated values to 4 decimal places. 5. Observe the pattern of the values as \( x \) approaches 6 to estimate the limit. Example \( x \) values: - Values on the left of 6: 5.9, 5.95, 5.99, 5.999 - Values on the right of 6: 6.1, 6.05, 6.01, 6.001 Calculate \( f(x) = \frac{\sqrt{10 - x} - 4}{{x - 6}} \) for each \( x \), and tabulate the results. ### Table of Values: | \( x \) | \( \frac{\sqrt{10 - x} - 4}{{x - 6}} \) | |---------------|------------------------------------------| | 5.9 | Value | | 5.95 | Value | | 5.99 | Value | | 5.999 | Value | | 6.001 | Value | | 6.01 | Value | | 6.05 | Value | | 6.1 | Value | Finally, analyze the values in the table to determine the estimated limit of the function as \( x \) approaches 6.
Transcribed Image Text:**Calculating the Limit Using a Table of Values** To estimate the limit of the function as \( x \) approaches 6, create a table of values using 8 values—4 values approaching 6 from the left and 4 values approaching 6 from the right. Use a calculator to determine and round off all values to 4 decimal places. The function to be evaluated is: $$ \lim_{{x \to 6}} \frac{\sqrt{10 - x} - 4}{{x - 6}} $$ ### Steps: 1. Choose 4 values of \( x \) slightly less than 6. 2. Choose 4 values of \( x \) slightly greater than 6. 3. Evaluate the function for each chosen \( x \). 4. Round the calculated values to 4 decimal places. 5. Observe the pattern of the values as \( x \) approaches 6 to estimate the limit. Example \( x \) values: - Values on the left of 6: 5.9, 5.95, 5.99, 5.999 - Values on the right of 6: 6.1, 6.05, 6.01, 6.001 Calculate \( f(x) = \frac{\sqrt{10 - x} - 4}{{x - 6}} \) for each \( x \), and tabulate the results. ### Table of Values: | \( x \) | \( \frac{\sqrt{10 - x} - 4}{{x - 6}} \) | |---------------|------------------------------------------| | 5.9 | Value | | 5.95 | Value | | 5.99 | Value | | 5.999 | Value | | 6.001 | Value | | 6.01 | Value | | 6.05 | Value | | 6.1 | Value | Finally, analyze the values in the table to determine the estimated limit of the function as \( x \) approaches 6.
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