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

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

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limit as x approaches infinity of e^x-3x

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

\infty

Solution steps

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

Apply the following algebraic property

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

e^{x} - 3 x = e^{x} (1 - \frac{3 x}{e ^{x}})

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

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

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

= \infty \cdot 1

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 1 + lim (\frac{3 x}{1 - x})

x \to 0 + lim (\frac{2}{x ^{3}})

θ \to \frac{5 π}{6} lim (cos (θ))

x \to 1 + lim (12 ∣ 2 x - 1 ∣ + a)

x \to 0 lim (x^{2} + 4 - 2)

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