Mastering Olympiad Mathematics
A collection of intriguing competition level problems for secondary school students.
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Tuesday, April 28, 2015
Calculate $\displaystyle \lim_{x \to \infty} (\sin \sqrt{x+1}-\sin \sqrt{x})$
Calculate $\displaystyle \lim_{x \to \infty} (\sin \sqrt{x+1}-\sin \sqrt{x})$.
Let:
[MATH]L=\lim_{x\to\infty}\left(\sin\left(\sqrt{x+1} \right)-\sin\left(\sqrt{x} \right) \right)[/MATH]
Application of the sum-to-product identity:
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