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Let’s check out your problem:

lim_(x rarr oo)(sqrt(x^(2)-2x)-x)=

lim⁡x→∞(x2−2x−x)= \lim _{x \rightarrow \infty}\left(\sqrt{x^{2}-2 x}-x\right)=

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Csc, sec, and cot of special anglesright chevron icon

Full solution

Q. lim⁡x→∞(x2−2x−x)= \lim _{x \rightarrow \infty}\left(\sqrt{x^{2}-2 x}-x\right)=
  1. Factor out xx: Step 11: Factor out xx from the square root to simplify the expression.
  2. Approaching infinity: Step 22: Since xx is approaching infinity, 2x\frac{2}{x} approaches 00.
  3. Simplify expression: Step 33: Simplify the expression inside the square root.
  4. Square root of x2x^2: Step 44: The square root of x2x^2 is xx, but we need to consider that xx is approaching infinity, so it's positive.
  5. Subtract xx: Step 55: Subtract xx from xx.
  6. Limit of constant: Step 66: The limit of a constant is the constant itself.

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