Evaluate limx→22x2−6x+4−2x2−x+10.

To evaluate the limit

\[
\lim_{{x \to 2}} \left( 2x^2 - 6x + 4 - 2x^2 - x + 10 \right),
\]

we can follow these steps:

### Step 1: Simplify the Expression
Let's first simplify the expression inside the limit:

\[
2x^2 - 6x + 4 - 2x^2 - x + 10
\]

Combine like terms:

\[
(2x^2 - 2x^2) + (-6x - x) + (4 + 10)
\]

This simplifies to:

\[
-7x + 14
\]

### Step 2: Evaluate the Limit
Now, the expression is much simpler:

\[
\lim_{{x \to 2}} (-7x + 14)
\]

Substitute \( x = 2 \):

\[
-7(2) + 14 = -14 + 14 = 0
\]

### Final Answer
The limit is:

\[
\boxed{0}
\]

Would you like any further details or have any questions?

### Relative Questions
1. How can you simplify polynomial expressions before taking a limit?
2. What are common techniques for evaluating limits involving subtraction of functions?
3. How do you handle limits at points where the function is continuous?
4. Can limits be used to determine points of continuity for a function?
5. How would this limit change if there was a division by a variable expression?

### Tip
When simplifying expressions for limits, always combine like terms to reduce the function to its simplest form before substituting the limit value.

Learn how to evaluate the limit of the polynomial expression 2x^2 - 6x + 4 - 2x^2 - x + 10 as x approaches 2. This problem covers key concepts in limits and polynomial expressions, including techniques for simplification and substitution. Suitable for advanced high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation