What is the limit as x approaches infinity of (1.1^x)/x ?

The limit as x approaches infinity of (1.1^x)/x is infinity

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limit as x approaches infinity of (1.1^x)/x

x \to \infty lim (\frac{1. 1 ^{x}}{x})

\infty

Solution steps

x \to \infty lim (\frac{1. 1 ^{x}}{x})

Apply L'Hopital's Rule

= x \to \infty lim (\frac{0.09531 \dots \cdot 1. 1 ^{x}}{1})

Simplify

= x \to \infty lim (0.09531 \dots \cdot 1. 1^{x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 0.09531 \dots \cdot x \to \infty lim (1. 1^{x})

Apply the common limit:

x \to \infty lim (a^{x}) = \infty, a > 1

= 0.09531 \dots \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

What is the limit as x approaches infinity of (1.1^x)/x ?
The limit as x approaches infinity of (1.1^x)/x is infinity