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

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

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

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

1

Solution steps

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

x \to \infty lim (1) = 1

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

= \frac{1}{1}

Simplify

= 1

f (x) = arctan (2 x)

\frac{d}{d x} (arccos (4 x^{3}))

\frac{d ^{2}}{d x ^{2}} (x^{2} sin (x))

\int \frac{1}{( x + y ) ^{2}} d x

n = 1 \sum \infty (- 1)^{n + 1}

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