Is every differentiable function continuous?

Explanation

To determine whether every differentiable function is continuous, we can follow these steps:

### Step 1: Understand the Definitions
- **Differentiable Function**: A function \( f(x) \) is said to be differentiable at a point \( a \) if the derivative \( f'(a) \) exists. This means that the limit
\[ f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h} \]
exists.
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