Math Problem Statement

Tentukan lim (x -> 2^-) f(x) berdasarkan grafik yang diberikan.

Solution

The problem asks for the limit of the function f(x)f(x) as xx approaches 2 from the left (x2x \to 2^-).

Let's analyze the graph:

  1. From the left side of x=2x = 2, the function follows a straight line that goes up to the point (2,3)(2, 3) with a filled dot, which means the function value is defined at that point.
  2. As xx approaches 2 from the left (x2x \to 2^-), the y-value of the function approaches 3.

Thus, the limit is:

limx2f(x)=3\lim_{x \to 2^-} f(x) = 3

The options provided are:

  • a. Tidak Ada (Does not exist)
  • b. 1
  • c. 0

Since none of these options match 3, the correct choice would be that the limit does not exist based on the given options.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

  1. What is the significance of filled and open circles in graph limits?
  2. How do you determine the limit of a function as xx approaches from the right?
  3. How can discontinuities affect the limit of a function?
  4. What does it mean when a limit does not exist?
  5. How can limits be used to define derivatives?

Tip: Always check the direction (left-hand or right-hand) when evaluating limits from one side!

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Math Problem Analysis

Mathematical Concepts

Limits
Continuity
Graphical Interpretation

Formulas

\lim_{x \to a^-} f(x)
Left-hand limit

Theorems

Limit Theorem
Continuity at a point

Suitable Grade Level

Grades 10-12