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

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

limit as x approaches-1-of (x+5)/(x+1)

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

- \infty

Solution steps

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

\frac{x + 5}{x + 1} = (x + 5) \frac{1}{x + 1}

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

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

With the exception of indeterminate form

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

x \to - 1 - lim (x + 5) = 4

x \to - 1 - lim (\frac{1}{x + 1}) = - \infty

= 4 (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

x \to - 3 lim (4 x)

x \to 1 lim (3 x^{3} + 5)

n \to \infty lim (\frac{5}{n})

x \to 0 lim (1 + 3 x)

x \to 1 lim (1 + x^{3})

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