Math Help - Limit problem.

1. Limit problem.

Hi, I´m having trouble solving this limit, without using the L´Hospital.

$limit_{x\to\infty}(\frac{2x+3}{2x+1})^x$

I tried dividing it into a sum and using Newtons binomial, but i arrived at

$limit_{x\to\infty}(\frac{4,481}{1+(1/2x)})^x$

which i am not able to solve. The answer should be e.

2. Re: Limit problem.

Hey HK47.

Hint: Separate the fraction by using (2x+3)/(2x+1) = (2x + 1 + 2)/(2x+1) = 1 + 2/(2x+1) and look at the formula for e in terms of (1 + 1/n)^n.

3. Re: Limit problem.

Thanks, expanded the binomial and discovered, that the constant doesnt contribute into the result.

$lim_x\to\infty{(1+\frac{1}{x+C})^x}=e$

Problem solved.

4. Re: Limit problem.

Try using the code:

\lim_{x\to c}f(x)