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anonymous
 4 years ago
Evaluate the limit. As x approaches infinity, the limit of x minus the square root of x^2 minus x minus 1.
anonymous
 4 years ago
Evaluate the limit. As x approaches infinity, the limit of x minus the square root of x^2 minus x minus 1.

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow \infty}x\sqrt{x ^{2}x1}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I know the answer, I just need to see how to get it. (1/2)

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0multiply by\[\frac{x+\sqrt{x^2x1}}{x+\sqrt{x^2x1}}\]

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0\[x\sqrt{x^2x1}\cdot\frac{x+\sqrt{x^2x1}}{x+\sqrt{x^2x1}}=\frac{x^2(x^2x1)}{x+\sqrt{x^2x1}}\]

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0\[=\frac{x+1}{x+\sqrt{x^2x1}}=\frac{x+1}{x+x\sqrt{1\frac1x\frac1{x^2}}}\]divide top and bottom of the fraction by x:\[=\frac{1+\frac1x}{1+\sqrt{1\frac1x\frac1{x^2}}}\]now evaluate the limit

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0remember \[(a/\infty) = 0\]
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