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Limit of the function (x/(1+2*x))^x

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              x
     /   x   \ 
 lim |-------| 
x->oo\1 + 2*x/

\lim_{x \to \infty} \left(\frac{x}{2 x + 1}\right)^{x}

Limit((x/(1 + 2*x))^x, x, oo, dir='-')

Lopital's rule

There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type

The graph

Plot the graph

Rapid solution [src]

0

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to \infty} \left(\frac{x}{2 x + 1}\right)^{x} = 0

\lim_{x \to 0^-} \left(\frac{x}{2 x + 1}\right)^{x} = 1

\lim_{x \to 0^+} \left(\frac{x}{2 x + 1}\right)^{x} = 1

\lim_{x \to 1^-} \left(\frac{x}{2 x + 1}\right)^{x} = \frac{1}{3}

\lim_{x \to 1^+} \left(\frac{x}{2 x + 1}\right)^{x} = \frac{1}{3}

\lim_{x \to -\infty} \left(\frac{x}{2 x + 1}\right)^{x} = \infty

The graph