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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

x \to \infty lim ((- 3)^{n})

x \to 0 + lim (3 e^{x} + cos (2 x))

x \to 0 lim (\frac{x + 12}{x + 6})

x \to 3 + lim ((3 - x) \cdot ln (x - 3))

x \to 0 lim (\frac{tan ( 9 x )}{sin ( 6 x )})

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