What is the limit as x approaches infinity of e^x-ex ?

The limit as x approaches infinity of e^x-ex is infinity

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limit as x approaches infinity of e^x-ex

x \to \infty lim (e^{x} - e x)

\infty

Solution steps

x \to \infty lim (e^{x} - e x)

Factor out

e^{x}

from

e^{x} - e x : e^{x} (1 - \frac{e x}{e ^{x}})

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

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

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

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

= \infty \cdot 1

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to - \infty lim (\frac{4 x ^{2} + 5 x}{x})

x \to 0 lim (2 - 6 x + 4 x^{2})

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

x \to 0 lim (\frac{4}{sin ( x )})

x \to 0 + lim (\frac{ln ( x )}{x - 1})

What is the limit as x approaches infinity of e^x-ex ?
The limit as x approaches infinity of e^x-ex is infinity