Consider the function `f(x)=x^(3)`. To find the limit as `x to 1`.

Options

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

Answer

To find the limit of the function \( f(x) = x^3 \) as \( x \) approaches 1, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the function**: We have the function \( f(x) = x^3 \).

2. **Set up the limit**: We want to find \( \lim_{x \to 1} f(x) \).

3. **Substitute the value of \( x \)**: Since the function \( f(x) = x^3 \) is continuous, we can directly substitute \( x = 1 \) into the function:
\[ f(1) = 1^3 \]

4. **Calculate the result**: Now, calculate \( 1^3 \):
\[ 1^3 = 1 \]

5. **Conclude the limit**: Therefore, we find that:
\[ \lim_{x \to 1} f(x) = 1 \]

### Final Answer:
\[ \lim_{x \to 1} f(x) = 1 \]