What is the limit as x approaches infinity of e^x-2x ?

The limit as x approaches infinity of e^x-2x is infinity

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limit as x approaches infinity of e^x-2x

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

\infty

Solution steps

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

Apply the following algebraic property

: a + b = a (1 + \frac{b}{a})

e^{x} - 2 x = e^{x} (1 - \frac{2 x}{e ^{x}})

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

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

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

= \infty \cdot 1

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\frac{d}{d x} (2 x - \frac{1}{x ^{2}})

\int x cot (x) csc (x) d x

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

\frac{\partial}{\partial x} (750 + 6 x - 7 y)

x^{2} - 3 x + 3, y = x

What is the limit as x approaches infinity of e^x-2x ?
The limit as x approaches infinity of e^x-2x is infinity