(1) $$ \lim _{x \rightarrow 0^{+}} \frac{\sin \sqrt{x}}{x}=\lim _{x \rightarrow 0^{-}} $$

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Calculate or simplify the expression $$ \lim_{x \rightarrow 0^{+}} \frac{\sin \sqrt{x}}{x} $$.
Evaluate the limit by following steps:
- step0: Evaluate using L'Hopital's rule:
  $$\lim _{x\rightarrow 0^{+}}\left(\frac{\sin\left(\sqrt{x}\right)}{x}\right)$$
- step1: Use the L'Hopital's rule:
  $$\lim _{x\rightarrow 0^{+}}\left(\frac{\frac{d}{dx}\left(\sin\left(\sqrt{x}\right)\right)}{\frac{d}{dx}\left(x\right)}\right)$$
- step2: Find the derivative:
  $$\lim _{x\rightarrow 0^{+}}\left(\frac{\frac{\cos\left(\sqrt{x}\right)}{2\sqrt{x}}}{1}\right)$$
- step3: Simplify the expression:
  $$\lim _{x\rightarrow 0^{+}}\left(\frac{\cos\left(\sqrt{x}\right)}{2\sqrt{x}}\right)$$
- step4: Rewrite the expression:
  $$\frac{\lim _{x\rightarrow 0^{+}}\left(\cos\left(\sqrt{x}\right)\right)}{\lim _{x\rightarrow 0^{+}}\left(2\sqrt{x}\right)}$$
- step5: Calculate:
  $$\frac{1}{\lim _{x\rightarrow 0^{+}}\left(2\sqrt{x}\right)}$$
- step6: Calculate:
  $$+\infty$$
When $$ x $$ approaches 0 from the right, the limit of $$ \frac{\sin \sqrt{x}}{x} $$ is positive infinity.
The limit $$ \lim_{x \rightarrow 0^{+}} \frac{\sin \sqrt{x}}{x} $$ is positive infinity.

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