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lim(x to 0) (x^(4) + x^(2) - 2x + 1) is ...

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

A

0

B

1

C

2

D

`-1`

Text Solution

AI Generated Solution

The correct Answer is:
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 \( 1 \).
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