Limit evaluation for oscillating function I want to evaluate the following oscillating limit x tends to infinity $$\sin(\sqrt{x+1})-\sin(\sqrt{x})$$
I tried evaluating this limit using trigonometric transformations but didn't arrive at the answer

$$\sqrt{x+1}-\sqrt{x}=\frac{(\sqrt{x+1}-\sqrt{x})(\sqrt{x+1}+\sqrt{x})}{\sqrt{x+1}+\sqrt{x}}=\frac{x+1-x}{\sqrt{x+1}+\sqrt{x}}=\frac{1}{\sqrt{x+1}+\sqrt{x}}$$
