What is the limit as x approaches 3+of (x-4)/(3-x) ?

The limit as x approaches 3+of (x-4)/(3-x) is infinity

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limit as x approaches 3+of (x-4)/(3-x)

x \to 3 + lim (\frac{x - 4}{3 - x})

\infty

Solution steps

x \to 3 + lim (\frac{x - 4}{3 - x})

\frac{x - 4}{3 - x} = (x - 4) \frac{1}{3 - x}

= x \to 3 + lim ((x - 4) \frac{1}{3 - x})

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

x \to 3 + lim (x - 4) = - 1

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

= (- 1) (- \infty)

Apply Infinity Property:

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

= \infty

What is the limit as x approaches 3+of (x-4)/(3-x) ?
The limit as x approaches 3+of (x-4)/(3-x) is infinity