Find `lim_(x to 0+) "|x|"/x`

Answer

To find the limit \( \lim_{x \to 0^+} \frac{|x|}{x} \), we can follow these steps:

### Step 1: Understand the expression
The expression involves the absolute value of \( x \), denoted as \( |x| \). Since we are taking the limit as \( x \) approaches \( 0 \) from the positive side (denoted as \( 0^+ \)), we know that \( x \) is always positive in this case.

### Step 2: Simplify the absolute value
For \( x > 0 \), the absolute value function behaves as follows:
\[ |x| = x \]
Thus, we can rewrite the limit:
\[ \lim_{x \to 0^+} \frac{|x|}{x} = \lim_{x \to 0^+} \frac{x}{x} \]

### Step 3: Simplify the fraction
Now, we simplify the fraction:
\[ \frac{x}{x} = 1 \quad \text{(for } x \neq 0\text{)} \]
So, we can rewrite the limit as:
\[ \lim_{x \to 0^+} 1 \]

### Step 4: Evaluate the limit
Since the limit of a constant is simply the constant itself, we have:
\[ \lim_{x \to 0^+} 1 = 1 \]

### Final Answer
Thus, the limit is:
\[ \boxed{1} \]