What is the limit as x approaches-5-of ((-7x))/(x+5) ?

The limit as x approaches-5-of ((-7x))/(x+5) is -infinity

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limit as x approaches-5-of ((-7x))/(x+5)

x \to - 5 - lim (\frac{( - 7 x )}{x + 5})

- \infty

Solution steps

x \to - 5 - lim (\frac{- 7 x}{x + 5})

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

= - 7 \cdot x \to - 5 - lim (\frac{x}{x + 5})

Divide by highest denominator power:

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

= - 7 \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

= - 7 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

\int \frac{1}{x ^{3} + 3 x ^{2} + 7 x + 5} d x

\int_{0}^{1} 2 π (x^{5} - x^{6}) d x

(x y^{3} + x^{2} y)^{3}

x \to 4 lim (f (x))

\frac{d}{d x} (\frac{1}{2} ln (x^{2} + 1))

What is the limit as x approaches-5-of ((-7x))/(x+5) ?
The limit as x approaches-5-of ((-7x))/(x+5) is -infinity