use the table of values to estimate lim f(x), lim f(x), and lim f(x).\n x→6⁻ x→6⁺ x→6\n| x | 5.9 | 5.99 |…

use the table of values to estimate lim f(x), lim f(x), and lim f(x).\n x→6⁻ x→6⁺ x→6\n| x | 5.9 | 5.99 | 5.999 | 5.9999 | 6.0001 | 6.001 | 6.01 | 6.1 |\n| f(x) | 8.9 | 8.99 | 8.999 | 8.9999 | 9.0001 | 9.001 | 9.01 | 9.1 |\nlim f(x)=\n x→6⁻

use the table of values to estimate lim f(x), lim f(x), and lim f(x).\n x→6⁻ x→6⁺ x→6\n| x | 5.9 | 5.99 | 5.999 | 5.9999 | 6.0001 | 6.001 | 6.01 | 6.1 |\n| f(x) | 8.9 | 8.99 | 8.999 | 8.9999 | 9.0001 | 9.001 | 9.01 | 9.1 |\nlim f(x)=\n x→6⁻

Answer

Explanation:

Step1: Analyze left - hand limit values

As (x) approaches (6) from the left ((x\to6^{-})), the (x) - values are (5.9,5.99,5.999,5.9999). The corresponding (f(x)) - values are (8.9,8.99,8.999,8.9999).

Step2: Determine left - hand limit

As (x) gets closer and closer to (6) from the left, (f(x)) gets closer and closer to (9). So, (\lim_{x\to6^{-}}f(x)=9).

Step3: Analyze right - hand limit values

As (x) approaches (6) from the right ((x\to6^{+})), the (x) - values are (6.0001,6.001,6.01,6.1). The corresponding (f(x)) - values are (9.0001,9.001,9.01,9.1).

Step4: Determine right - hand limit

As (x) gets closer and closer to (6) from the right, (f(x)) gets closer and closer to (9). So, (\lim_{x\to6^{+}}f(x)=9).

Step5: Determine overall limit

Since (\lim_{x\to6^{-}}f(x)=\lim_{x\to6^{+}}f(x) = 9), then (\lim_{x\to6}f(x)=9).

Answer:

(\lim_{x\to6^{-}}f(x)=9), (\lim_{x\to6^{+}}f(x)=9), (\lim_{x\to6}f(x)=9)