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

The limit as x approaches infinity of (1-3/x)^{x^2} is 0

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

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

0

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

0

= 0

x \to 2 + lim (\frac{3 - x}{x - 2})

x \to 0 lim (\frac{x ( x + 1 )}{x})

x \to 0 lim (x e^{\frac{- 1}{x}})

x \to 1 lim (x^{2} - 5 x + 6)

x \to \infty - lim (x)

What is the limit as x approaches infinity of (1-3/x)^{x^2} ?
The limit as x approaches infinity of (1-3/x)^{x^2} is 0