What is the limit as x approaches infinity of (e^{5x}+x^2)/(e^{5x)-x} ?

The limit as x approaches infinity of (e^{5x}+x^2)/(e^{5x)-x} is 1

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limit as x approaches infinity of (e^{5x}+x^2)/(e^{5x)-x}

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

1

Solution steps

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

Apply L'Hopital's Rule

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

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

Apply L'Hopital's Rule

: x \to \infty lim (\frac{25 e ^{5 x} + 2}{25 e ^{5 x}})

= x \to \infty lim (\frac{25 e ^{5 x} + 2}{25 e ^{5 x}})

Apply L'Hopital's Rule

: x \to \infty lim (\frac{125 e ^{5 x}}{125 e ^{5 x}})

= x \to \infty lim (\frac{125 e ^{5 x}}{125 e ^{5 x}})

Simplify

= x \to \infty lim (1)

x \to a lim c = c

= 1

\frac{d}{d t} (2 sin^{3} (t))

y = (x + 1)^{2}, (- 1, 0)

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

y = \frac{x - 1}{x + 1}

x \to 0 - lim (arccos (e^{- x^{2}}))

What is the limit as x approaches infinity of (e^{5x}+x^2)/(e^{5x)-x} ?
The limit as x approaches infinity of (e^{5x}+x^2)/(e^{5x)-x} is 1