(7) $$ \quad \lim _{h \rightarrow 0} \frac{\sin (x+h)-\sin (x)}{h}= $$

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To evaluate the limit:

$$
\lim_{h \rightarrow 0} \frac{\sin(x + h) - \sin(x)}{h}
$$

This limit represents the derivative of the sine function at the point $$ x $$. Let's compute it step by step.

**Step 1: Expand $$\sin(x + h)$$ using the sine addition formula**

$$
\sin(x + h) = \sin(x)\cos(h) + \cos(x)\sin(h)
$$

**Step 2: Substitute the expansion back into the limit**

$$
\lim_{h \rightarrow 0} \frac{\sin(x)\cos(h) + \cos(x)\sin(h) - \sin(x)}{h} = \lim_{h \rightarrow 0} \frac{\sin(x)(\cos(h) - 1) + \cos(x)\sin(h)}{h}
$$

**Step 3: Split the limit into two parts**

$$
\lim_{h \rightarrow 0} \left[ \sin(x) \cdot \frac{\cos(h) - 1}{h} + \cos(x) \cdot \frac{\sin(h)}{h} \right]
$$

**Step 4: Evaluate each limit separately**

1. $$\lim_{h \rightarrow 0} \frac{\cos(h) - 1}{h} = 0$$
2. $$\lim_{h \rightarrow 0} \frac{\sin(h)}{h} = 1$$

**Step 5: Combine the results**

$$
\sin(x) \cdot 0 + \cos(x) \cdot 1 = \cos(x)
$$

**Conclusion:**

$$
\lim_{h \rightarrow 0} \frac{\sin(x + h) - \sin(x)}{h} = \cos(x)
$$

**Answer:**  
The limit is equal to cos x.
The limit is equal to cos x.

(7) \( \quad \lim _{h \rightarrow 0} \frac{\sin (x+h)-\sin (x)}{h}= \)

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