What is the limit as x approaches infinity of a/x ?

The limit as x approaches infinity of a/x is 0

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limit as x approaches infinity of a/x

x \to \infty lim (\frac{a}{x})

0

Solution steps

x \to \infty lim (\frac{a}{x})

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

= a \cdot x \to \infty lim (\frac{1}{x})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= a \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( x )}

x \to \infty lim (1) = 1

x \to \infty lim (x) = \infty

= a \frac{1}{\infty}

Simplify

a \frac{1}{\infty} : 0

= 0

\frac{d}{d x} (\frac{x}{x + \frac{a}{x}})

\frac{d}{d x} (\frac{- 5}{x ^{3}})

n = 0 \sum \infty (0.1)^{n}

\frac{d}{d x} (cos^{3} (x^{2} - x))

What is the limit as x approaches infinity of a/x ?
The limit as x approaches infinity of a/x is 0