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

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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) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

\frac{d}{d x} ((4 x^{3} + 5 x)^{4})

f (x) = x ln (x)

\int - e^{- x} + 1 d x

\int_{- 6}^{6} (36 - x^{2}) d x

\frac{d}{d x} (\frac{x - 1}{2 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