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

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

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limit as x approaches infinity of x-2^x

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

- \infty

Solution steps

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

Apply the following algebraic property

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

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

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

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

x \to \infty lim (2^{x}) = \infty

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

= \infty \cdot (- 1)

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

y^{^{''}} + 8 y^{^{'}} + 9 y = 0

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

x \to 1 lim (ln (1))

x \to 0 lim (5 - \frac{∣ x ∣}{x})

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