Limit problem with [(sqrt(x+1)-1)/x]

Thread starter thereddevils
Start date Apr 5, 2010
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Limit

AI Thread Summary

The limit of the expression (sqrt(x+1)-1)/x as x approaches infinity can be evaluated by multiplying the numerator and denominator by (sqrt(x+1)+1). This simplification leads to the expression (x+1-1)/(x(sqrt(x+1)+1)), which simplifies to 1/(sqrt(x+1)+1). As x approaches infinity, sqrt(x+1) approaches sqrt(x), resulting in the limit converging to 0. Therefore, the limit is 0.

Apr 5, 2010

thereddevils

Homework Statement

Find the limit of lim (x approach infinity) [(sqrt(x+1)-1)/x]

Homework Equations

The Attempt at a Solution

i try to reduce it to a form where i can put the x in but to no avail ?

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Apr 5, 2010

Mark44

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Multiply by 1 in the form of (sqrt(x + 1) + 1) over itself.

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