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

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

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

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

1

Solution steps

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

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

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

x \to \infty lim (1) = 1

= 1 \cdot 1

Simplify

= 1

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