`lim_(x to 0) (x^(4) + x^(2) - 2x + 1)` is eqal to

Options

A. 0
B. 1
C. 2
D. `-1`

Answer

To solve the limit \( \lim_{x \to 0} (x^4 + x^2 - 2x + 1) \), we will evaluate the expression by substituting \( x \) with \( 0 \).

### Step-by-Step Solution:

1. **Substitute \( x = 0 \)**:
\[ x^4 + x^2 - 2x + 1 \quad \text{becomes} \quad 0^4 + 0^2 - 2(0) + 1 \]

2. **Calculate each term**:
- \( 0^4 = 0 \)
- \( 0^2 = 0 \)
- \( -2(0) = 0 \)
- The constant term is \( 1 \)

3. **Combine the results**:
\[ 0 + 0 + 0 + 1 = 1 \]

4. **Conclusion**:
\[ \lim_{x \to 0} (x^4 + x^2 - 2x + 1) = 1 \]

Thus, the limit is equal to \( 1 \).