Math Problem Statement

Tentukan \lim_{x \to 2} f(x) berdasarkan grafik.

Solution

The problem in the image asks to determine the limit limx2f(x)\lim_{x \to 2} f(x) from the graph.

Let's analyze the graph:

  1. The graph is piecewise and shows a function with two lines intersecting the vertical line at x=2x = 2.

  2. To find the limit, we need to look at the values of f(x)f(x) as xx approaches 2 from both sides (left and right):

    • From the left (x2x \to 2^-): The graph approaches the value y=3y = 3 as xx approaches 2 from the left.
    • From the right (x2+x \to 2^+): The graph approaches the value y=1y = 1 as xx approaches 2 from the right.

Since the left-hand limit (33) and the right-hand limit (11) are not equal, the limit does not exist.

Therefore, the correct answer is d. Tidak Ada (There is no limit).

Would you like further details on this explanation or any other clarification?

Here are five related questions:

  1. What is the definition of a limit?
  2. How can you determine if a function is continuous at a point?
  3. What happens if the left and right limits are different at a point?
  4. Can the limit exist if the function is not defined at the point itself?
  5. What is the difference between a one-sided and two-sided limit?

Tip: When evaluating limits from a graph, always check both sides of the point to see if the function approaches the same value from the left and right.

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Math Problem Analysis

Mathematical Concepts

Limits
Piecewise Functions

Formulas

-

Theorems

Limit definition
One-sided limits

Suitable Grade Level

Grades 11-12 (Pre-Calculus/Calculus)