Differences of roots

Task number: 2868

Determine the following limits.

  • Variant 1

    \(\displaystyle \lim_{n\to\infty} \sqrt{n+5}-\sqrt{n-1}\)

  • Variant 2

    \(\displaystyle \lim_{n\to\infty} \sqrt[3]{(n+1)^2}-\sqrt[3]{(n-1)^2}\)

  • Variant 3

    \(\displaystyle \lim_{n\to\infty} \sqrt{n}\left(\sqrt{n+1}-\sqrt{n} \right)\)

  • Variant 4

    \(\displaystyle \lim_{n\to\infty} \sqrt{n^2+n}-\sqrt{n}\)

  • Variant 5

    \(\displaystyle \lim_{n\to\infty} \left(n\left(\sqrt{n-3}-n\right)\right)\)

  • Variant 6

    \(\displaystyle \lim_{n\to\infty} \left(\sin\sqrt{n+1}- \sin\sqrt{n}\right)\)

Difficulty level: Moderate task
Routine calculation training
Cs translation
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