What is the limit as x approaches-infinity of-5/x ?

The limit as x approaches-infinity of-5/x is 0

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limit as x approaches-infinity of-5/x

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

0

Solution steps

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

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

= - 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

= - 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

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

Simplify

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

= 0

x \to 0 lim (\frac{( 1 - cos ( x ) )}{3 x ^{2}})

x \to 4 lim (\frac{4 - 4 + 3 x}{4 - x})

x \to - 1 + lim (2^{\frac{1}{x + 1}})

x \to 25 lim (5 - x)

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

What is the limit as x approaches-infinity of-5/x ?
The limit as x approaches-infinity of-5/x is 0