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

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

Popular >

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

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

- \infty

Solution steps

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

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

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

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

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

= (- 2) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

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

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

x \to 0 lim (x + \frac{4}{x ^{2}})

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

x \to 0 lim ((1 + x^{2})^{\frac{1}{1 - c o s ( x )}})

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