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

\int - 4 csc^{2} (x) d x

n = 1 \sum \infty \frac{n}{3 n ^{2} + 1}

\frac{\partial}{\partial x} (ln (x + y) + x \cdot cos (y))

\frac{d}{d x} (ln (x e^{- 9 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