Math Problem Statement

Tentukan limit-limit berikut: lim (x -> -1) (3x^2 - 2x + 1)

Solution

The question shown in the image is in Indonesian, asking to determine limits. The specific part visible is:

Tentukan limit-limit berikut
a. limx1(3x22x+1)\lim_{x \to -1} (3x^2 - 2x + 1)

Let's solve this limit step by step.

Step 1: Substitution

We can try direct substitution since the function is a polynomial, which is continuous. Substituting x=1x = -1 into the expression:

3(1)22(1)+1=3(1)+2+1=3+2+1=63(-1)^2 - 2(-1) + 1 = 3(1) + 2 + 1 = 3 + 2 + 1 = 6

Final Answer:

limx1(3x22x+1)=6\lim_{x \to -1} (3x^2 - 2x + 1) = 6

Would you like more details on this calculation, or do you have any further questions?

Here are 5 follow-up questions that could extend your understanding of this topic:

  1. What happens if a limit approaches infinity or a point where the function is undefined?
  2. How can we determine the limits involving rational functions where direct substitution results in indeterminate forms?
  3. Can we apply L'Hopital's Rule to compute limits involving fractions?
  4. What are one-sided limits, and how are they different from standard limits?
  5. How can limits be applied to understand the behavior of a function near discontinuities?

Tip: Always check if a function is continuous at the point you're evaluating the limit. For continuous functions like polynomials, direct substitution will always work.

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Math Problem Analysis

Mathematical Concepts

Limits
Polynomial Functions
Continuity

Formulas

Direct substitution for continuous functions

Theorems

Continuity of polynomials

Suitable Grade Level

Grades 11-12 or introductory university level