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

Thread starter thereddevils
Start date Apr 5, 2010
Tags

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 ?

Physics news on Phys.org

Apr 5, 2010

Mark44

Mentor

Insights Author

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

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks

View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks

View full post »