18. $$ \lim _{x \rightarrow 0} \frac{1-\cos (x)}{\sin (x)}= $$

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Calculate the limit $$ \lim_{x \rightarrow 0} \frac{1-\cos(x)}{\sin(x)} $$.
Evaluate the limit by following steps:
- step0: Evaluate using L'Hopital's rule:
  $$\lim _{x\rightarrow 0}\left(\frac{1-\cos\left(x\right)}{\sin\left(x\right)}\right)$$
- step1: Use the L'Hopital's rule:
  $$\lim _{x\rightarrow 0}\left(\frac{\frac{d}{dx}\left(1-\cos\left(x\right)\right)}{\frac{d}{dx}\left(\sin\left(x\right)\right)}\right)$$
- step2: Find the derivative:
  $$\lim _{x\rightarrow 0}\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)$$
- step3: Rewrite the expression:
  $$\frac{\lim _{x\rightarrow 0}\left(\sin\left(x\right)\right)}{\lim _{x\rightarrow 0}\left(\cos\left(x\right)\right)}$$
- step4: Calculate:
  $$\frac{0}{\lim _{x\rightarrow 0}\left(\cos\left(x\right)\right)}$$
- step5: Calculate:
  $$\frac{0}{1}$$
- step6: Calculate:
  $$0$$
The limit of $$ \frac{1-\cos(x)}{\sin(x)} $$ as $$ x $$ approaches 0 is 0.
The limit is 0.

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