Math Problem Statement

\lim_{\cdot\rarr3} $$$$ \left(4x-6\right)

Solution

It looks like you're trying to find the limit of the function 4x64x - 6 as xx approaches a certain value, but the limit expression is incomplete.

Let me fill it in and evaluate the limit properly:

limx3(4x6)\lim_{x \to 3} \left(4x - 6\right)

Solution

To find this limit, we can substitute x=3x = 3 directly into the linear function:

limx3(4x6)=4(3)6=126=6\lim_{x \to 3} (4x - 6) = 4(3) - 6 = 12 - 6 = 6

Thus, the value of the limit is:

limx3(4x6)=6\lim_{x \to 3} (4x - 6) = 6


Would you like me to explain why substitution works in this case, or do you have any other questions?

Related Questions:

  1. What is the limit of 5x+25x + 2 as xx approaches 44?
  2. How do you find the limit of a quadratic function as xx approaches a given value?
  3. What is the limit of x29x3\frac{x^2 - 9}{x - 3} as xx approaches 33?
  4. How do you handle limits when substitution results in an indeterminate form?
  5. What is the difference between one-sided and two-sided limits?

Tip: Direct substitution in limits works when the function is continuous at the point of interest. If not, more advanced techniques like factoring, conjugation, or L'Hôpital's rule may be needed.

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Math Problem Analysis

Mathematical Concepts

Limits
Linear Functions

Formulas

\lim_{x \to a} f(x) = f(a) for continuous functions

Theorems

Direct Substitution Theorem

Suitable Grade Level

Grades 11-12