What is the limit as x approaches infinity of 1/((2x+1)^{1/x)} ?

The limit as x approaches infinity of 1/((2x+1)^{1/x)} is 1

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limit as x approaches infinity of 1/((2x+1)^{1/x)}

x \to \infty lim (\frac{1}{( 2 x + 1 ) ^{\frac{1}{x}}})

1

Solution steps

x \to \infty lim (\frac{1}{( 2 x + 1 ) ^{\frac{1}{x}}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( ( 2 x + 1 ) ^{\frac{1}{x}} )}

x \to \infty lim (1) = 1

x \to \infty lim ((2 x + 1)^{\frac{1}{x}}) = 1

= \frac{1}{1}

Simplify

= 1

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What is the limit as x approaches infinity of 1/((2x+1)^{1/x)} ?
The limit as x approaches infinity of 1/((2x+1)^{1/x)} is 1