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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

: x \to - \infty lim (\frac{1 + 6 e ^{2 x}}{1 + e ^{2 x} \cdot 2})

= x \to - \infty lim (\frac{1 + 6 e ^{2 x}}{1 + e ^{2 x} \cdot 2})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to - \infty} ( 1 + 6 e ^{2 x} )}{lim _{x \to - \infty} ( 1 + e ^{2 x} \cdot 2 )}

x \to - \infty lim (1 + 6 e^{2 x}) = 1

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

= \frac{1}{1}

Simplify

= 1

x, x = 8 - \frac{1}{4} y^{2}

\frac{\partial}{\partial x} (x^{y})

\int - e^{2 x} x d x

\frac{\partial}{\partial x} (y^{6} cos (3 x))

\int \frac{x ^{3}}{3 ( 1 + x ^{2} )} d x

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