What is the limit as x approaches infinity of (1+(0.02)/x)^{2x} ?

The limit as x approaches infinity of (1+(0.02)/x)^{2x} is 1.04081…

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limit as x approaches infinity of (1+(0.02)/x)^{2x}

x \to \infty lim ((1 + \frac{0.02}{x})^{2 x})

1.04081 \dots

Solution steps

x \to \infty lim ((1 + \frac{0.02}{x})^{2 x})

Apply exponent rules

= x \to \infty lim (e^{2 x l n (1 + \frac{0.02}{x})})

Apply the Limit Chain Rule:

1.04081 \dots

= 1.04081 \dots

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

x \to \infty lim ((\frac{2 x + 1}{x + 3})^{\frac{3 x + 2}{x - 5}})

x \to 0 lim (\frac{sin ( x )}{arcsin ( x )})

x \to - \infty lim (x + (x))

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

What is the limit as x approaches infinity of (1+(0.02)/x)^{2x} ?
The limit as x approaches infinity of (1+(0.02)/x)^{2x} is 1.04081…