What is the limit as x approaches infinity of (1+1/(x^3))^{2x^2} ?

The limit as x approaches infinity of (1+1/(x^3))^{2x^2} is 1

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limit as x approaches infinity of (1+1/(x^3))^{2x^2}

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

1

Solution steps

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

Apply exponent rules

= x \to \infty lim (e^{2 x^{2} l n (1 + \frac{1}{x ^{3}})})

Apply the Limit Chain Rule:

1

= 1

\frac{d}{d x} (e^{\frac{3}{2} x} (\frac{13}{17} cos (2 x) + b sin (2 x)) + \frac{4}{17} e^{2 x})

\int x^{2} - 6 x + 9 d x

\int x (x - 3)^{5} d x

y = 1 + 3 x, 3 \leq x \leq 9

y = 10 x^{2}, y = x^{2} + 12

What is the limit as x approaches infinity of (1+1/(x^3))^{2x^2} ?
The limit as x approaches infinity of (1+1/(x^3))^{2x^2} is 1