Question

\\\lim_{x \to 2} (2x^2 - 6x + 2)\\

Explanation:

🆕 New Concept Discovered: Limits by Direct Substitution
Finding the value a function approaches by plugging in the target number.

Step 1: Identify the limit expression

The problem asks us to evaluate the limit of a polynomial function as \( x \) approaches \( 2 \):

\[ \lim_{x \to 2} (2x^2 - 6x + 2) \]

Step 2: Apply direct substitution

Since polynomial functions are continuous everywhere, we can find the limit by directly substituting \( x = 2 \) into the expression:

\[ 2(2)^2 - 6(2) + 2 \]

Step 3: Simplify the expression

Calculate each term step-by-step:

1. Evaluate the exponent:

\[ 2(4) - 6(2) + 2 \]

1. Multiply the terms:

\[ 8 - 12 + 2 \]

1. Add and subtract from left to right:

\[ -4 + 2 = -2 \]

Answer:

\[ -2 \]