What is the limit as x approaches infinity of 1/(5x) ?

The limit as x approaches infinity of 1/(5x) is 0

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limit as x approaches infinity of 1/(5x)

x \to \infty lim (\frac{1}{5 x})

0

Solution steps

x \to \infty lim (\frac{1}{5 x})

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

= \frac{1}{5} \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

= \frac{1}{5} \cdot \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( x )}

x \to \infty lim (1) = 1

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

= \frac{1}{5} \cdot \frac{1}{\infty}

Simplify

\frac{1}{5} \cdot \frac{1}{\infty} : 0

= 0

\int (x \cdot sin (x^{2} + 1)) d x

\frac{d}{d x} (e^{\frac{- x ^{2}}{2}})

2 x + \frac{4 x}{3 x - 1}

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

2 sec (2 x)

What is the limit as x approaches infinity of 1/(5x) ?
The limit as x approaches infinity of 1/(5x) is 0