Math Problem Statement

Limit x^3 + 1 = 26 as x approaches -3

Solution

The problem shown in the image is:

limx3x3+1=26\lim_{x \to -3} x^3 + 1 = 26

To solve this, we simply substitute x=3x = -3 into the expression x3+1x^3 + 1.

  1. x3=(3)3=27x^3 = (-3)^3 = -27
  2. x3+1=27+1=26x^3 + 1 = -27 + 1 = -26

However, this results in 26-26, not 26 as indicated in the equation. So the equation limx3x3+1=26\lim_{x \to -3} x^3 + 1 = 26 is not true, since substituting x=3x = -3 gives 26-26, not 26.

Would you like further clarification or additional details?

Here are 5 questions you might explore next:

  1. What is the formal definition of a limit?
  2. How can limits be used to analyze the behavior of functions as they approach a point?
  3. What happens if we have a discontinuity at x=3x = -3?
  4. How could we modify the function so that the limit equals 26?
  5. What are some other examples of cubic functions with limits at specific points?

Tip: Always verify if substituting the limit point directly into a polynomial function yields the correct result, as limits of polynomials are straightforward.

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Math Problem Analysis

Mathematical Concepts

Limits
Polynomials

Formulas

Limit as x approaches a value
Cubic functions: x^3

Theorems

Limit Theorem for Polynomials

Suitable Grade Level

Grades 10-12