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

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

limit as x approaches infinity of x-e^x

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

- \infty

Solution steps

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

Apply the following algebraic property

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

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

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

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

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

= \infty \cdot (- 1)

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

(3, - 4), (5, 2)

\int \frac{x ^{2}}{1 - x ^{2}} d x

\frac{\partial}{\partial x} (2 g (x) \cdot (x^{- 2}) \cdot (\frac{D}{L}))

f (x) = \frac{7}{x}, at x = 4

f (x) = 2 x^{3} + 4 x^{2} - 5 x - 3, at x = - 1

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