What is the limit as x approaches 3-of (x-1)/(x-3) ?

The limit as x approaches 3-of (x-1)/(x-3) is -infinity

limit as x approaches 3-of (x-1)/(x-3)

x \to 3 - lim (\frac{x - 1}{x - 3})

- \infty

Solution steps

x \to 3 - lim (\frac{x - 1}{x - 3})

\frac{x - 1}{x - 3} = (x - 1) \frac{1}{x - 3}

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

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

x \to 3 - lim (x - 1) = 2

x \to 3 - lim (\frac{1}{x - 3}) = - \infty

= 2 (- \infty)

Apply Infinity Property:

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

= - \infty

x \to 0 lim (x^{4} sin (\frac{π}{x}))

x \to 2 - lim (ln (x))

x \to 4 lim (\frac{( 3 x ^{2} - 8 x - 16 )}{2 x ^{2} - 9 x + 4})

x \to 0 lim ((1 + \frac{2}{x ^{3}})^{x})

x \to \frac{π}{2} + lim (\frac{x}{cot ( x )})

What is the limit as x approaches 3-of (x-1)/(x-3) ?
The limit as x approaches 3-of (x-1)/(x-3) is -infinity