What is the limit as x approaches-5-of (-3x)/(x+5) ?

The limit as x approaches-5-of (-3x)/(x+5) is -infinity

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limit as x approaches-5-of (-3x)/(x+5)

x \to - 5 - lim (\frac{- 3 x}{x + 5})

- \infty

Solution steps

x \to - 5 - lim (\frac{- 3 x}{x + 5})

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

= - 3 \cdot x \to - 5 - lim (\frac{x}{x + 5})

Divide by highest denominator power:

\frac{1}{1 + \frac{5}{x}}

= - 3 \cdot x \to - 5 - lim (\frac{1}{1 + \frac{5}{x}})

For

x

approaching

- 5

from the left

, x < - 5 \Rightarrow 1 + \frac{5}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= - 3 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

h \to 0 lim (\frac{cos ( \frac{3 π}{2} + h ) - cos ( \frac{3 π}{2} )}{h})

x \to 2 lim (x + 7)

x \to 0 lim (\frac{( cos ( 5 x ) - 1 )}{x sin ( x )})

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

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

What is the limit as x approaches-5-of (-3x)/(x+5) ?
The limit as x approaches-5-of (-3x)/(x+5) is -infinity