What is the limit as x approaches 5-of (x-1)/(2x-10) ?

The limit as x approaches 5-of (x-1)/(2x-10) is -infinity

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limit as x approaches 5-of (x-1)/(2x-10)

x \to 5 - lim (\frac{x - 1}{2 x - 10})

- \infty

Solution steps

x \to 5 - lim (\frac{x - 1}{2 x - 10})

\frac{x - 1}{2 x - 10} = (x - 1) \frac{1}{2 x - 10}

= x \to 5 - lim ((x - 1) \frac{1}{2 x - 10})

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 5 - lim (x - 1) \cdot x \to 5 - lim (\frac{1}{2 x - 10})

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

x \to 5 - lim (\frac{1}{2 x - 10}) = - \infty

= 4 (- \infty)

Apply Infinity Property:

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

= - \infty

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

x \to 0 lim (x - e^{x} + 1)

x \to - 2 lim (\frac{1}{4 - x ^{2}})

x \to 4 lim (\frac{3 x ^{2} - 17 x + 20}{4 x ^{2} - 25 + 36})

x \to 0 + lim (\frac{e ^{- x}}{x})

What is the limit as x approaches 5-of (x-1)/(2x-10) ?
The limit as x approaches 5-of (x-1)/(2x-10) is -infinity