Find the limit. $$ \lim _{h \rightarrow 0}\left(\frac{\sqrt{11+h}-\sqrt{11}}{h}\right) $$

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Calculate the limit $$ \lim_{h ightarrow 0} \frac{\sqrt{11+h}-\sqrt{11}}{h} $$.
Evaluate the limit by following steps:
- step0: Evaluate using transformations:
  $$\lim _{hightarrow 0}\left(\frac{\sqrt{11+h}-\sqrt{11}}{h}ight)$$
- step1: Multiply by the Conjugate:
  $$\lim _{hightarrow 0}\left(\frac{1}{\sqrt{11+h}+\sqrt{11}}ight)$$
- step2: Rewrite the expression:
  $$\frac{\lim _{hightarrow 0}\left(1ight)}{\lim _{hightarrow 0}\left(\sqrt{11+h}+\sqrt{11}ight)}$$
- step3: Evaluate:
  $$\frac{1}{\lim _{hightarrow 0}\left(\sqrt{11+h}+\sqrt{11}ight)}$$
- step4: Evaluate:
  $$\frac{1}{2\sqrt{11}}$$
- step5: Multiply by the Conjugate:
  $$\frac{\sqrt{11}}{2\sqrt{11}	imes \sqrt{11}}$$
- step6: Multiply the numbers:
  $$\frac{\sqrt{11}}{22}$$
The limit of the expression $$\frac{\sqrt{11+h}-\sqrt{11}}{h}$$ as $$h$$ approaches 0 is $$\frac{\sqrt{11}}{22}$$.
The limit is $$\frac{\sqrt{11}}{22}$$.

Find the limit.

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