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

The limit as x approaches infinity of (1+b/x)^{kx} is e^{bk}

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

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

e^{bk}

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{bk}

= e^{bk}

What is the limit as x approaches infinity of (1+b/x)^{kx} ?
The limit as x approaches infinity of (1+b/x)^{kx} is e^{bk}