Math Problem Statement

just answer

The table above gives values of a function f at selected values of x. Which of the following conclusions is supported by the data in the table? A) lim(x→6) f(x) = 0, B) lim(x→6) f(x) = 6.

Solution

The correct answer is A) limx6f(x)=0\lim_{x \to 6} f(x) = 0.

Explanation: As xx approaches 6 from both sides (values of xx close to 6 are given in the table), the values of f(x)f(x) decrease and get closer to 0. Therefore, the limit as xx approaches 6 is 0.

Do you want more details or have any questions?

Here are 5 related questions:

  1. What does it mean for a limit to exist as xx approaches a specific value?
  2. How can you determine a limit from a table of values?
  3. What happens if the left-hand limit and right-hand limit differ?
  4. Can a function have a limit at a point where it is undefined?
  5. How is the behavior of a function near a point different from the value of the function at that point?

Tip: Always check the values approaching from both sides when determining limits from tables.

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Math Problem Analysis

Mathematical Concepts

Limits
Functions
Approaching values

Formulas

lim(x→a) f(x) = L

Theorems

Limit Theorem
Squeeze Theorem

Suitable Grade Level

Grades 11-12