Evaluate the following limits:
`lim_(xrarr1)(6x^(2)-4x+3)`

Options

A. 5
B. 4
C. 3
D. 2

Answer

To evaluate the limit \( \lim_{x \to 1} (6x^2 - 4x + 3) \), we can follow these steps:

### Step 1: Substitute \( x = 1 \) into the expression
We will directly substitute \( x = 1 \) into the polynomial \( 6x^2 - 4x + 3 \).

\[ 6(1)^2 - 4(1) + 3 \]

### Step 2: Calculate \( 6(1)^2 \)
Calculating \( 6(1)^2 \):

\[ 6 \cdot 1 = 6 \]

### Step 3: Calculate \( -4(1) \)
Calculating \( -4(1) \):

\[ -4 \cdot 1 = -4 \]

### Step 4: Combine the results
Now we combine the results from Steps 2 and 3 along with the constant term \( +3 \):

\[ 6 - 4 + 3 \]

### Step 5: Simplify the expression
Now we simplify:

\[ 6 - 4 = 2 \]
\[ 2 + 3 = 5 \]

### Final Result
Thus, the limit is:

\[ \lim_{x \to 1} (6x^2 - 4x + 3) = 5 \]