Use continuity to evaluate the limit: $\underset{x\to 2}{lim}3x^2-5x+4$.

• A. $2$
• B. $6$
• C. $6$
• D. $6-10+4=0$

Answer: (C)

Verified step by step guidance

1. Step 1: Recognize that the function given, \(3x^2 - 5x + 4\), is a polynomial. Polynomials are continuous everywhere, meaning we can directly substitute the value of \(x\) into the function to evaluate the limit.
2. Step 2: Substitute \(x = 2\) into the polynomial \(3x^2 - 5x + 4\). This involves replacing \(x\) with \(2\) in each term of the polynomial.
3. Step 3: Compute \(3x^2\) by substituting \(x = 2\). This gives \(3(2)^2\), which simplifies to \(3 \cdot 4\).
4. Step 4: Compute \(-5x\) by substituting \(x = 2\). This gives \(-5(2)\), which simplifies to \(-10\).
5. Step 5: Add the results from \(3x^2\), \(-5x\), and the constant \(+4\) together to find the value of the limit. This involves summing \(12\), \(-10\), and \(4\).