What is the limit as x approaches infinity of 3^x-x ?

The limit as x approaches infinity of 3^x-x is infinity

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limit as x approaches infinity of 3^x-x

x \to \infty lim (3^{x} - x)

\infty

Solution steps

x \to \infty lim (3^{x} - x)

Factor out

3^{x}

from

3^{x} - x : 3^{x} (1 - \frac{x}{3 ^{x}})

= x \to \infty lim (3^{x} (1 - \frac{x}{3 ^{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 (3^{x}) \cdot x \to \infty lim (1 - \frac{x}{3 ^{x}})

x \to \infty lim (3^{x}) = \infty

x \to \infty lim (1 - \frac{x}{3 ^{x}}) = 1

= \infty \cdot 1

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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

\frac{\partial}{\partial x} (y^{5} cos (6 x) \cdot 6)

\frac{d}{d x} (\frac{1 + ln ( x )}{1 - ln ( x )})

\int \frac{4}{4 - x ^{2}} d x

- \frac{6 x}{x ^{2} + 1}, at x = 1

What is the limit as x approaches infinity of 3^x-x ?
The limit as x approaches infinity of 3^x-x is infinity