`lim_(x to 0)(abs(0))/x` is equal to :

Options

A. 1
B. -1
C. 0
D. does not exist

Answer

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

### Step 1: Evaluate the absolute value
First, we need to evaluate \( |0| \). The absolute value of zero is:
\[ |0| = 0 \]

### Step 2: Substitute the absolute value into the limit
Now we substitute this value back into the limit:
\[ \lim_{x \to 0} \frac{|0|}{x} = \lim_{x \to 0} \frac{0}{x} \]

### Step 3: Simplify the expression
The expression simplifies to:
\[ \frac{0}{x} = 0 \]
for any non-zero \( x \).

### Step 4: Evaluate the limit
Now we can evaluate the limit:
\[ \lim_{x \to 0} 0 = 0 \]

### Final Answer
Thus, the limit is:
\[ \lim_{x \to 0} \frac{|0|}{x} = 0 \]